id	sid	eid	entity	type
ejpam-5621	1	1	european journal	ORG
ejpam-5621	1	2	2025	DATE
ejpam-5621	1	3	18	CARDINAL
ejpam-5621	1	4	2	CARDINAL
ejpam-5621	1	5	5621	CARDINAL
ejpam-5621	1	6	1307-5543	DATE
ejpam-5621	1	7	new york	GPE
ejpam-5621	1	8	habeeb ibrahim1	PERSON
ejpam-5621	1	9	mohammed e. dafaalla2,∗	PERSON
ejpam-5621	1	10	osman abdalla adam osman3	PERSON
ejpam-5621	1	11	ashraf	PERSON
ejpam-5621	2	1	s. elshreif4	PERSON
ejpam-5621	3	1	1	CARDINAL
ejpam-5621	3	2	51452	DATE
ejpam-5621	3	3	saudi arabia	GPE
ejpam-5621	5	1	2020	DATE
ejpam-5621	5	2	35j60	CARDINAL
ejpam-5621	5	3	35b65	CARDINAL
ejpam-5621	5	4	46e35	DATE
ejpam-5621	5	5	1	CARDINAL
ejpam-5621	7	1	div(|gm|p−2 gm	PERSON
ejpam-5621	7	2	ω	CARDINAL
ejpam-5621	7	3	1	CARDINAL
ejpam-5621	7	4	1	CARDINAL
ejpam-5621	8	1	ω ∈	ORG
ejpam-5621	9	1	gm	ORG
ejpam-5621	9	2	g1	ORG
ejpam-5621	10	1	|ξ|2 ⩽ e(x)ξ.ξ	PERSON
ejpam-5621	10	2	2	CARDINAL
ejpam-5621	10	3	∈	ORG
ejpam-5621	11	1	1	CARDINAL
ejpam-5621	11	2	2	CARDINAL
ejpam-5621	11	3	1	CARDINAL
ejpam-5621	11	4	3	CARDINAL
ejpam-5621	11	5	p(x	PERSON
ejpam-5621	12	1	4	CARDINAL
ejpam-5621	14	1	∗corresponding	GPE
ejpam-5621	15	1	ha.ibrahim@qu.edu.sa	ORG
ejpam-5621	15	2	h. ibrahim	PERSON
ejpam-5621	15	3	m. e. dafaalla	PERSON
ejpam-5621	15	4	o.osman@qu.edu.sa	CARDINAL
ejpam-5621	15	5	a. adam osman	PERSON
ejpam-5621	15	6	ae.mohammad@qu.edu.sa	CARDINAL
ejpam-5621	15	7	a. s. elshreif	PERSON
ejpam-5621	16	1	1	CARDINAL
ejpam-5621	16	2	2025	CARDINAL
ejpam-5621	17	1	h. ibrahim et al	PERSON
ejpam-5621	18	1	j. pure	PERSON
ejpam-5621	18	2	18	CARDINAL
ejpam-5621	18	3	2	CARDINAL
ejpam-5621	18	4	2025	CARDINAL
ejpam-5621	18	5	5621 2	DATE
ejpam-5621	18	6	16	CARDINAL
ejpam-5621	19	1	lq	ORG
ejpam-5621	19	2	1	CARDINAL
ejpam-5621	20	1	8	CARDINAL
ejpam-5621	21	1	aij	PRODUCT
ejpam-5621	21	2	bmo spaces	ORG
ejpam-5621	23	1	1	CARDINAL
ejpam-5621	26	1	y)− ēbr	PERSON
ejpam-5621	26	2	ēbr(x	ORG
ejpam-5621	26	3	br(x	GPE
ejpam-5621	27	1	9–11	CARDINAL
ejpam-5621	27	2	second	ORDINAL
ejpam-5621	28	1	vmo	ORG
ejpam-5621	28	2	bmo	GPE
ejpam-5621	31	1	1	CARDINAL
ejpam-5621	32	1	2	CARDINAL
ejpam-5621	34	1	1	CARDINAL
ejpam-5621	36	1	2	CARDINAL
ejpam-5621	36	2	1	CARDINAL
ejpam-5621	36	3	∈w 1,p	NORP
ejpam-5621	36	4	ω	ORDINAL
ejpam-5621	37	1	1	CARDINAL
ejpam-5621	37	2	b3 ⊂ ω	ORG
ejpam-5621	38	1	∫ b3 |gm|q dx	PERSON
ejpam-5621	38	2	3	CARDINAL
ejpam-5621	39	1	8	CARDINAL
ejpam-5621	41	1	∈w 1,p	EVENT
ejpam-5621	41	2	∈	ORG
ejpam-5621	43	1	1	CARDINAL
ejpam-5621	43	2	0	CARDINAL
ejpam-5621	44	1	h. ibrahim et al	PERSON
ejpam-5621	45	1	j. pure	PERSON
ejpam-5621	45	2	18	CARDINAL
ejpam-5621	45	3	2	CARDINAL
ejpam-5621	45	4	2025	CARDINAL
ejpam-5621	45	5	5621 3	DATE
ejpam-5621	45	6	16	CARDINAL
ejpam-5621	45	7	1	CARDINAL
ejpam-5621	46	1	i1	ORG
ejpam-5621	47	1	2	CARDINAL
ejpam-5621	47	2	i1 = ∫ b3 ζp(e∇vm.∇vm)p\2dx ≥ 1 α ∫ b3	ORG
ejpam-5621	47	3	dx	ORG
ejpam-5621	48	1	2	CARDINAL
ejpam-5621	49	1	dx ≤ τ ∫ b3	ORG
ejpam-5621	49	2	|∇vm|p	CARDINAL
ejpam-5621	51	1	|∇vm|p	CARDINAL
ejpam-5621	51	2	dx	ORG
ejpam-5621	52	1	i4	ORG
ejpam-5621	54	1	j ≤ 4	FAC
ejpam-5621	54	2	1	CARDINAL
ejpam-5621	54	3	∫ b3	PERSON
ejpam-5621	54	4	∫ b3	PERSON
ejpam-5621	54	5	vpmdx+	ORG
ejpam-5621	54	6	1	CARDINAL
ejpam-5621	54	7	4α	CARDINAL
ejpam-5621	57	1	1	CARDINAL
ejpam-5621	58	1	h. ibrahim et al	PERSON
ejpam-5621	59	1	j. pure	PERSON
ejpam-5621	59	2	18	CARDINAL
ejpam-5621	59	3	2	CARDINAL
ejpam-5621	59	4	2025	CARDINAL
ejpam-5621	59	5	5621 4	DATE
ejpam-5621	59	6	16	CARDINAL
ejpam-5621	59	7	2	CARDINAL
ejpam-5621	59	8	∈	ORG
ejpam-5621	59	9	1,p	ORDINAL
ejpam-5621	59	10	loc (ω	ORG
ejpam-5621	59	11	1	CARDINAL
ejpam-5621	61	1	1	CARDINAL
ejpam-5621	61	2	∮	ORDINAL
ejpam-5621	61	3	|∇vm|p	CARDINAL
ejpam-5621	61	4	1	CARDINAL
ejpam-5621	61	5	1	CARDINAL
ejpam-5621	62	1	two	CARDINAL
ejpam-5621	62	2	two	CARDINAL
ejpam-5621	62	3	6	CARDINAL
ejpam-5621	63	1	|∇vm|p	CARDINAL
ejpam-5621	63	2	1	CARDINAL
ejpam-5621	64	1	1	CARDINAL
ejpam-5621	64	2	4	CARDINAL
ejpam-5621	65	1	∈	ORG
ejpam-5621	65	2	0	CARDINAL
ejpam-5621	65	3	0	CARDINAL
ejpam-5621	66	1	0	CARDINAL
ejpam-5621	68	1	3	CARDINAL
ejpam-5621	71	1	∈ a(λ	ORG
ejpam-5621	71	2	25	CARDINAL
ejpam-5621	72	1	|∇vm|p	CARDINAL
ejpam-5621	72	2	1	CARDINAL
ejpam-5621	73	1	1	CARDINAL
ejpam-5621	74	1	⋃	DATE
ejpam-5621	74	2	2j+2b0	CARDINAL
ejpam-5621	74	3	1	CARDINAL
ejpam-5621	74	4	2	DATE
ejpam-5621	75	1	1	CARDINAL
ejpam-5621	76	1	+ 1	DATE
ejpam-5621	76	2	1/q1 ≤	QUANTITY
ejpam-5621	78	1	∮	CARDINAL
ejpam-5621	78	2	+ 1	DATE
ejpam-5621	79	1	h. ibrahim et al	PERSON
ejpam-5621	80	1	j. pure	PERSON
ejpam-5621	80	2	18	CARDINAL
ejpam-5621	80	3	2	CARDINAL
ejpam-5621	80	4	2025	CARDINAL
ejpam-5621	80	5	5621 5	DATE
ejpam-5621	80	6	16	CARDINAL
ejpam-5621	81	1	2 6n	CARDINAL
ejpam-5621	81	2	5	CARDINAL
ejpam-5621	81	3	ω ∈ b1	ORG
ejpam-5621	81	4	1/25 ≤	MONEY
ejpam-5621	82	1	25bp(ω	CARDINAL
ejpam-5621	83	1	1	CARDINAL
ejpam-5621	83	2	2 5	CARDINAL
ejpam-5621	83	3	2 6n	CARDINAL
ejpam-5621	83	4	1	CARDINAL
ejpam-5621	83	5	2	DATE
ejpam-5621	84	1	6	CARDINAL
ejpam-5621	84	2	4	CARDINAL
ejpam-5621	84	3	5	CARDINAL
ejpam-5621	84	4	6	CARDINAL
ejpam-5621	85	1	1	CARDINAL
ejpam-5621	85	2	1	CARDINAL
ejpam-5621	85	3	1	CARDINAL
ejpam-5621	86	1	ω	ORDINAL
ejpam-5621	86	2	1 q1 ≤ 2 6n	QUANTITY
ejpam-5621	86	3	1	CARDINAL
ejpam-5621	87	1	two	CARDINAL
ejpam-5621	87	2	4	CARDINAL
ejpam-5621	88	1	26n/pλ0	DATE
ejpam-5621	89	1	ω ∈ a(λ	ORG
ejpam-5621	90	1	lim	PERSON
ejpam-5621	91	1	0	CARDINAL
ejpam-5621	92	1	∈	ORG
ejpam-5621	92	2	0	CARDINAL
ejpam-5621	92	3	1/25	CARDINAL
ejpam-5621	93	1	8	CARDINAL
ejpam-5621	99	1	ω ∈ a(λ	ORG
ejpam-5621	100	1	vitali	PERSON
ejpam-5621	100	2	bpxi	GPE
ejpam-5621	100	3	xi)}i∈n	GPE
ejpam-5621	103	1	h. ibrahim et al	PERSON
ejpam-5621	104	1	j. pure	PERSON
ejpam-5621	104	2	18	CARDINAL
ejpam-5621	104	3	2	CARDINAL
ejpam-5621	104	4	2025	CARDINAL
ejpam-5621	104	5	5621 6	CARDINAL
ejpam-5621	104	6	16	CARDINAL
ejpam-5621	104	7	4	CARDINAL
ejpam-5621	105	1	6	CARDINAL
ejpam-5621	106	1	1	CARDINAL
ejpam-5621	106	2	4} |∇vm|pdx+	MONEY
ejpam-5621	107	1	4	CARDINAL
ejpam-5621	107	2	2q1/[1−	CARDINAL
ejpam-5621	107	3	1/2)p	CARDINAL
ejpam-5621	109	1	the lemma above,(∫	LOC
ejpam-5621	111	1	7	CARDINAL
ejpam-5621	111	2	one	CARDINAL
ejpam-5621	111	3	1	CARDINAL
ejpam-5621	111	4	1	CARDINAL
ejpam-5621	112	1	6	CARDINAL
ejpam-5621	112	2	two	CARDINAL
ejpam-5621	112	3	2p λp	CARDINAL
ejpam-5621	112	4	|∇vm|>λ/4	PERSON
ejpam-5621	112	5	1/2)q1	CARDINAL
ejpam-5621	114	1	1/2)q1	CARDINAL
ejpam-5621	115	1	1	CARDINAL
ejpam-5621	116	1	12	CARDINAL
ejpam-5621	116	2	13	CARDINAL
ejpam-5621	117	1	3	CARDINAL
ejpam-5621	117	2	2 6n	CARDINAL
ejpam-5621	118	1	∈	ORG
ejpam-5621	120	1	h. ibrahim et al	PERSON
ejpam-5621	121	1	j. pure	PERSON
ejpam-5621	121	2	18	CARDINAL
ejpam-5621	121	3	2	CARDINAL
ejpam-5621	121	4	2025	CARDINAL
ejpam-5621	121	5	5621 7	DATE
ejpam-5621	121	6	16	CARDINAL
ejpam-5621	121	7	1	CARDINAL
ejpam-5621	121	8	gm	ORG
ejpam-5621	122	1	3	CARDINAL
ejpam-5621	123	1	dx ≤ 1	PERSON
ejpam-5621	124	1	1	CARDINAL
ejpam-5621	124	2	2	DATE
ejpam-5621	124	3	3	DATE
ejpam-5621	124	4	2	CARDINAL
ejpam-5621	125	1	0	CARDINAL
ejpam-5621	126	1	bs	GPE
ejpam-5621	126	2	9	CARDINAL
ejpam-5621	127	1	3	CARDINAL
ejpam-5621	129	1	− gm ∈w 1,p	EVENT
ejpam-5621	130	1	0	CARDINAL
ejpam-5621	131	1	bs	GPE
ejpam-5621	132	1	∫ bs	ORG
ejpam-5621	132	2	∇umēbs∇um	PRODUCT
ejpam-5621	134	1	5	CARDINAL
ejpam-5621	134	2	∫ bs |∇vm|pdx	ORG
ejpam-5621	134	3	10	CARDINAL
ejpam-5621	134	4	1	CARDINAL
ejpam-5621	134	5	11	CARDINAL
ejpam-5621	134	6	0	CARDINAL
ejpam-5621	134	7	s/2	GPE
ejpam-5621	136	1	5	CARDINAL
ejpam-5621	137	1	0	CARDINAL
ejpam-5621	138	1	1	CARDINAL
ejpam-5621	138	2	ω	LOC
ejpam-5621	138	3	⊂ ω	ORG
ejpam-5621	138	4	∣∣e −	PERSON
ejpam-5621	138	5	∣∣dx ≤ δ	PERSON
ejpam-5621	138	6	12	CARDINAL
ejpam-5621	140	1	13	CARDINAL
ejpam-5621	140	2	n0	GPE
ejpam-5621	140	3	1	CARDINAL
ejpam-5621	140	4	1	CARDINAL
ejpam-5621	140	5	h. ibrahim	PERSON
ejpam-5621	142	1	j. pure	PERSON
ejpam-5621	142	2	18	CARDINAL
ejpam-5621	142	3	2	CARDINAL
ejpam-5621	142	4	2025	CARDINAL
ejpam-5621	142	5	5621 8	DATE
ejpam-5621	142	6	16	CARDINAL
ejpam-5621	143	1	1	CARDINAL
ejpam-5621	143	2	2	CARDINAL
ejpam-5621	143	3	4	CARDINAL
ejpam-5621	143	4	1	CARDINAL
ejpam-5621	143	5	ω	LOC
ejpam-5621	143	6	2	CARDINAL
ejpam-5621	144	1	2	CARDINAL
ejpam-5621	144	2	2	CARDINAL
ejpam-5621	144	3	.∇(u−	PERSON
ejpam-5621	145	1	−	PERSON
ejpam-5621	148	1	i1	ORG
ejpam-5621	149	1	two	CARDINAL
ejpam-5621	150	1	1	CARDINAL
ejpam-5621	150	2	2	CARDINAL
ejpam-5621	151	1	2	CARDINAL
ejpam-5621	151	2	η	PERSON
ejpam-5621	151	3	2 ēb2η	DATE
ejpam-5621	152	1	− η	PERSON
ejpam-5621	152	2	η ∈	PERSON
ejpam-5621	152	3	2	CARDINAL
ejpam-5621	152	4	1	CARDINAL
ejpam-5621	152	5	2	CARDINAL
ejpam-5621	153	1	2	CARDINAL
ejpam-5621	153	2	η	PERSON
ejpam-5621	153	3	2 ēb2η	DATE
ejpam-5621	154	1	− η	PERSON
ejpam-5621	156	1	η ∈	PERSON
ejpam-5621	156	2	0	CARDINAL
ejpam-5621	156	3	1	CARDINAL
ejpam-5621	158	1	ζ)(p−2)/2eζ	PERSON
ejpam-5621	158	2	∣∣∣ ≤	MONEY
ejpam-5621	160	1	|ζ|p−1	PRODUCT
ejpam-5621	161	1	each o	DATE
ejpam-5621	161	2	η ∈	PERSON
ejpam-5621	162	1	− ē ∣∣ p p−1	ORG
ejpam-5621	162	2	q2−p)/q2(∫	NORP
ejpam-5621	164	1	2α)(p 2+q2−p)/[q2(p−1	CARDINAL
ejpam-5621	164	2	h. ibrahim et al	PERSON
ejpam-5621	165	1	j. pure	PERSON
ejpam-5621	165	2	18	CARDINAL
ejpam-5621	165	3	2	CARDINAL
ejpam-5621	165	4	2025	CARDINAL
ejpam-5621	165	5	5621 9	DATE
ejpam-5621	165	6	16	CARDINAL
ejpam-5621	165	7	2	CARDINAL
ejpam-5621	165	8	3	CARDINAL
ejpam-5621	165	9	|∇vm|	CARDINAL
ejpam-5621	165	10	q2 dx	ORG
ejpam-5621	167	1	1	CARDINAL
ejpam-5621	168	1	1	CARDINAL
ejpam-5621	168	2	4	CARDINAL
ejpam-5621	168	3	13	CARDINAL
ejpam-5621	173	1	1 ≤ i ≤ 3	QUANTITY
ejpam-5621	173	2	2τ	CARDINAL
ejpam-5621	176	1	0	CARDINAL
ejpam-5621	176	2	1	CARDINAL
ejpam-5621	176	3	13):∫	CARDINAL
ejpam-5621	178	1	1	CARDINAL
ejpam-5621	178	2	2	CARDINAL
ejpam-5621	178	3	2	CARDINAL
ejpam-5621	178	4	1	CARDINAL
ejpam-5621	179	1	− ē	PERSON
ejpam-5621	179	2	14	CARDINAL
ejpam-5621	179	3	0 ≤	MONEY
ejpam-5621	179	4	1	CARDINAL
ejpam-5621	179	5	0	CARDINAL
ejpam-5621	179	6	1	DATE
ejpam-5621	179	7	2	DATE
ejpam-5621	179	8	3	CARDINAL
ejpam-5621	180	1	lemma 2	ORG
ejpam-5621	180	2	7	CARDINAL
ejpam-5621	181	1	6	CARDINAL
ejpam-5621	181	2	greater than zero	CARDINAL
ejpam-5621	181	3	0	CARDINAL
ejpam-5621	181	4	n0	GPE
ejpam-5621	181	5	ω	LOC
ejpam-5621	181	6	b3 i ⊂ ω	ORG
ejpam-5621	181	7	∣∣∣ ≤ n0	MONEY
ejpam-5621	183	1	15	CARDINAL
ejpam-5621	183	2	2	CARDINAL
ejpam-5621	185	1	h. ibrahim et al	PERSON
ejpam-5621	186	1	j. pure	PERSON
ejpam-5621	186	2	18	CARDINAL
ejpam-5621	186	3	2	CARDINAL
ejpam-5621	186	4	2025	CARDINAL
ejpam-5621	186	5	5621 10	DATE
ejpam-5621	186	6	16	CARDINAL
ejpam-5621	187	1	0	CARDINAL
ejpam-5621	187	2	1	DATE
ejpam-5621	187	3	2	DATE
ejpam-5621	187	4	3	DATE
ejpam-5621	187	5	23pzi	DATE
ejpam-5621	187	6	3pxix	PERSON
ejpam-5621	187	7	ei(x	PERSON
ejpam-5621	189	1	7	CARDINAL
ejpam-5621	189	2	14	CARDINAL
ejpam-5621	190	1	∣∣∣pdx ≤ 1	CARDINAL
ejpam-5621	192	1	1	CARDINAL
ejpam-5621	192	2	0	CARDINAL
ejpam-5621	192	3	|∇um| ≤	MONEY
ejpam-5621	192	4	∣∣∣p dx ≤	PERSON
ejpam-5621	192	5	1 23pxi	CARDINAL
ejpam-5621	192	6	∈	ORG
ejpam-5621	193	1	3	CARDINAL
ejpam-5621	195	1	4	CARDINAL
ejpam-5621	195	2	1	CARDINAL
ejpam-5621	195	3	1	CARDINAL
ejpam-5621	196	1	0	CARDINAL
ejpam-5621	196	2	gm	ORG
ejpam-5621	198	1	16	CARDINAL
ejpam-5621	198	2	gm	ORG
ejpam-5621	198	3	b4r(x0)	ORG
ejpam-5621	200	1	5	CARDINAL
ejpam-5621	200	2	14	CARDINAL
ejpam-5621	201	1	h. ibrahim et al	PERSON
ejpam-5621	202	1	j. pure	PERSON
ejpam-5621	202	2	18	CARDINAL
ejpam-5621	202	3	2	CARDINAL
ejpam-5621	202	4	2025	CARDINAL
ejpam-5621	202	5	5621 11	DATE
ejpam-5621	202	6	16	CARDINAL
ejpam-5621	204	1	3	CARDINAL
ejpam-5621	204	2	λ∗	PRODUCT
ejpam-5621	204	3	obtain∣∣{x	CARDINAL
ejpam-5621	204	4	∈	ORG
ejpam-5621	204	5	2n0λ	CARDINAL
ejpam-5621	204	6	2n0	CARDINAL
ejpam-5621	205	1	∣∣∣	CARDINAL
ejpam-5621	205	2	∈	ORG
ejpam-5621	205	3	∣∣∣∇(umλ	CARDINAL
ejpam-5621	205	4	∣∣∣ ≤ 1	MONEY
ejpam-5621	207	1	24nεp|b0	CARDINAL
ejpam-5621	209	1	lemma 2	ORG
ejpam-5621	209	2	2n0λ	CARDINAL
ejpam-5621	211	1	4 |}	QUANTITY
ejpam-5621	212	1	+ 1	DATE
ejpam-5621	215	1	⋃	DATE
ejpam-5621	215	2	∈	ORG
ejpam-5621	216	1	∈	ORG
ejpam-5621	216	2	2n0λ}| ≤ ∑	QUANTITY
ejpam-5621	216	3	2n0λ	CARDINAL
ejpam-5621	216	4	1	CARDINAL
ejpam-5621	216	5	x∈b2:|∇vm|>λ 4	DATE
ejpam-5621	217	1	x∈b2:|gm|	EVENT
ejpam-5621	217	2	4	CARDINAL
ejpam-5621	217	3	17	CARDINAL
ejpam-5621	219	1	∈	ORG
ejpam-5621	221	1	∈	ORG
ejpam-5621	221	2	2n0λ∗ µq−1	DATE
ejpam-5621	221	3	∈	ORG
ejpam-5621	222	1	∈	ORG
ejpam-5621	223	1	q−1 |{x ∈	PERSON
ejpam-5621	223	2	2n0λ}|	CARDINAL
ejpam-5621	224	1	λ∗	PRODUCT
ejpam-5621	225	1	|∇vm|p	CARDINAL
ejpam-5621	227	1	+ 1	DATE
ejpam-5621	228	1	18	CARDINAL
ejpam-5621	228	2	1	CARDINAL
ejpam-5621	232	1	+ 1	DATE
ejpam-5621	236	1	+ 1	DATE
ejpam-5621	237	1	h. ibrahim et al	PERSON
ejpam-5621	238	1	j. pure	PERSON
ejpam-5621	238	2	18	CARDINAL
ejpam-5621	238	3	2	CARDINAL
ejpam-5621	238	4	2025	CARDINAL
ejpam-5621	238	5	5621 12	DATE
ejpam-5621	238	6	16	CARDINAL
ejpam-5621	238	7	14	CARDINAL
ejpam-5621	238	8	1	CARDINAL
ejpam-5621	238	9	0	CARDINAL
ejpam-5621	241	1	j2	ORG
ejpam-5621	242	1	17	CARDINAL
ejpam-5621	242	2	j2 ≤ cεp {	ORG
ejpam-5621	242	3	0	CARDINAL
ejpam-5621	243	1	+ 1 δq1	DATE
ejpam-5621	243	2	0	CARDINAL
ejpam-5621	245	1	1	CARDINAL
ejpam-5621	245	2	j2 ≤ c1ε p ∫ b2 |∇um|qdx+ c2ε p ∫ b2 |fm|qdx	ORG
ejpam-5621	246	1	j1	ORG
ejpam-5621	246	2	|∇vm|qdx+ c3 ∫	PERSON
ejpam-5621	246	3	dx	ORG
ejpam-5621	246	4	c3 =	PERSON
ejpam-5621	247	1	15	CARDINAL
ejpam-5621	247	2	16	CARDINAL
ejpam-5621	247	3	first	ORDINAL
ejpam-5621	247	4	1/2	CARDINAL
ejpam-5621	249	1	1	CARDINAL
ejpam-5621	249	2	1	CARDINAL
ejpam-5621	249	3	greater than zero	CARDINAL
ejpam-5621	250	1	1+ε	CARDINAL
ejpam-5621	250	2	1+ε	CARDINAL
ejpam-5621	252	1	h. ibrahim et al	PERSON
ejpam-5621	253	1	j. pure	PERSON
ejpam-5621	253	2	18	CARDINAL
ejpam-5621	253	3	2	CARDINAL
ejpam-5621	253	4	2025	CARDINAL
ejpam-5621	253	5	5621 13	DATE
ejpam-5621	253	6	16	DATE
ejpam-5621	253	7	e(δ	ORG
ejpam-5621	253	8	gm	ORG
ejpam-5621	253	9	gm ∈ l 1+ϵ ϵ loc	ORG
ejpam-5621	259	1	ε dx	ORG
ejpam-5621	259	2	c̄	DATE
ejpam-5621	259	3	gm	ORG
ejpam-5621	262	1	2	CARDINAL
ejpam-5621	263	1	1/	CARDINAL
ejpam-5621	263	2	2x	CARDINAL
ejpam-5621	263	3	∈	ORG
ejpam-5621	264	1	2n0(λ∗	CARDINAL
ejpam-5621	266	1	1/2	CARDINAL
ejpam-5621	266	2	1/	CARDINAL
ejpam-5621	266	3	∈	ORG
ejpam-5621	267	1	2n0	CARDINAL
ejpam-5621	267	2	∈	ORG
ejpam-5621	267	3	1/2	CARDINAL
ejpam-5621	267	4	∈	ORG
ejpam-5621	267	5	∣∣∣	CARDINAL
ejpam-5621	267	6	1/{x	CARDINAL
ejpam-5621	267	7	∈	ORG
ejpam-5621	267	8	1/2	CARDINAL
ejpam-5621	272	1	24nε1+ε|b0	CARDINAL
ejpam-5621	273	1	n1+ε 0	DATE
ejpam-5621	273	2	3	CARDINAL
ejpam-5621	273	3	1/	CARDINAL
ejpam-5621	273	4	2x	CARDINAL
ejpam-5621	273	5	∈	ORG
ejpam-5621	273	6	s∑ m=1	TIME
ejpam-5621	274	1	2n0(λ∗	CARDINAL
ejpam-5621	275	1	1/2 ≤	QUANTITY
ejpam-5621	275	2	1	CARDINAL
ejpam-5621	276	1	s∑ m=1 |∇vm|1+δdx	DATE
ejpam-5621	276	2	c̄ = c̄(n	DATE
ejpam-5621	276	3	1 + ϵ	DATE
ejpam-5621	278	1	∈	ORG
ejpam-5621	278	2	s∑ m=1 |∇vm|	CARDINAL
ejpam-5621	278	3	1/	CARDINAL
ejpam-5621	278	4	2x	CARDINAL
ejpam-5621	278	5	∈	ORG
ejpam-5621	279	1	2n0(λ∗	CARDINAL
ejpam-5621	279	2	1/{2x	CARDINAL
ejpam-5621	279	3	∈	ORG
ejpam-5621	280	1	2n0(λ∗ +	DATE
ejpam-5621	280	2	1	CARDINAL
ejpam-5621	281	1	1	CARDINAL
ejpam-5621	281	2	1+ε	CARDINAL
ejpam-5621	281	3	1δ	CARDINAL
ejpam-5621	281	4	1+ε	CARDINAL
ejpam-5621	281	5	1	CARDINAL
ejpam-5621	281	6	1+ε	CARDINAL
ejpam-5621	281	7	19	CARDINAL
ejpam-5621	283	1	|∇vm|	TIME
ejpam-5621	283	2	1+ε	CARDINAL
ejpam-5621	283	3	1+ε	CARDINAL
ejpam-5621	283	4	0	CARDINAL
ejpam-5621	284	1	1+ε	CARDINAL
ejpam-5621	284	2	∈	ORG
ejpam-5621	284	3	1+ε	CARDINAL
ejpam-5621	285	1	0	CARDINAL
ejpam-5621	285	2	1+ε	CARDINAL
ejpam-5621	285	3	∈	ORG
ejpam-5621	285	4	1+ε	CARDINAL
ejpam-5621	285	5	2n0λ∗	CARDINAL
ejpam-5621	285	6	1+ε	CARDINAL
ejpam-5621	285	7	∈	ORG
ejpam-5621	286	1	1+ε	CARDINAL
ejpam-5621	287	1	0	CARDINAL
ejpam-5621	287	2	1+ε	CARDINAL
ejpam-5621	287	3	∈	ORG
ejpam-5621	287	4	1+ε	CARDINAL
ejpam-5621	287	5	2n0	PRODUCT
ejpam-5621	287	6	1+ε	CARDINAL
ejpam-5621	287	7	h. ibrahim et al	PERSON
ejpam-5621	288	1	j. pure	PERSON
ejpam-5621	288	2	18	CARDINAL
ejpam-5621	288	3	2	CARDINAL
ejpam-5621	288	4	2025	CARDINAL
ejpam-5621	288	5	5621 14	DATE
ejpam-5621	288	6	16	CARDINAL
ejpam-5621	288	7	1/2x	CARDINAL
ejpam-5621	288	8	∈	ORG
ejpam-5621	288	9	s∑ m=1	DATE
ejpam-5621	288	10	2n0(λ∗	CARDINAL
ejpam-5621	290	1	1/2	CARDINAL
ejpam-5621	293	1	1+ε	CARDINAL
ejpam-5621	293	2	26n	CARDINAL
ejpam-5621	293	3	1+ε	CARDINAL
ejpam-5621	294	1	1+ε	CARDINAL
ejpam-5621	296	1	1+ε	CARDINAL
ejpam-5621	297	1	1+ε	CARDINAL
ejpam-5621	297	2	1+ε	CARDINAL
ejpam-5621	297	3	1+ε	CARDINAL
ejpam-5621	297	4	1+ε	CARDINAL
ejpam-5621	297	5	1	CARDINAL
ejpam-5621	298	1	3	CARDINAL
ejpam-5621	298	2	1+ε	CARDINAL
ejpam-5621	299	1	1+ε	CARDINAL
ejpam-5621	300	1	1+ε	CARDINAL
ejpam-5621	300	2	1+ε	CARDINAL
ejpam-5621	300	3	1+ε	CARDINAL
ejpam-5621	300	4	1+ε	CARDINAL
ejpam-5621	300	5	1	CARDINAL
ejpam-5621	300	6	1+ε	CARDINAL
ejpam-5621	302	1	1+ε	CARDINAL
ejpam-5621	303	1	1+ε	CARDINAL
ejpam-5621	303	2	1+ε	CARDINAL
ejpam-5621	303	3	1+ε	CARDINAL
ejpam-5621	303	4	1+ε	CARDINAL
ejpam-5621	304	1	1+ε	CARDINAL
ejpam-5621	304	2	s∑ m=1 |vm|	DATE
ejpam-5621	304	3	1+ε	CARDINAL
ejpam-5621	304	4	s∑ m=1 |gm|(	PERCENT
ejpam-5621	304	5	1+ε	CARDINAL
ejpam-5621	304	6	c̄ = c̄(n	DATE
ejpam-5621	304	7	1 +	CARDINAL
ejpam-5621	304	8	1+ε	CARDINAL
ejpam-5621	305	1	j2 estimation	ORG
ejpam-5621	305	2	18	CARDINAL
ejpam-5621	306	1	1+ε	CARDINAL
ejpam-5621	306	2	1+ε	CARDINAL
ejpam-5621	306	3	1	CARDINAL
ejpam-5621	306	4	0	CARDINAL
ejpam-5621	307	1	|βdx	ORG
ejpam-5621	307	2	x∈rm:|f	ORG
ejpam-5621	307	3	1	CARDINAL
ejpam-5621	307	4	j2 ≤	ORG
ejpam-5621	307	5	1+ε	CARDINAL
ejpam-5621	308	1	s∑ m=1	DATE
ejpam-5621	308	2	1+ε	CARDINAL
ejpam-5621	308	3	1+ε	CARDINAL
ejpam-5621	308	4	s∑ m=1 |gm|(	PERCENT
ejpam-5621	308	5	1+ε	CARDINAL
ejpam-5621	308	6	h. ibrahim et al	PERSON
ejpam-5621	309	1	j. pure	PERSON
ejpam-5621	309	2	18	CARDINAL
ejpam-5621	309	3	2	CARDINAL
ejpam-5621	309	4	2025	CARDINAL
ejpam-5621	309	5	5621 15	DATE
ejpam-5621	309	6	16	CARDINAL
ejpam-5621	309	7	1 +	CARDINAL
ejpam-5621	309	8	1+ε	CARDINAL
ejpam-5621	309	9	1 +	CARDINAL
ejpam-5621	309	10	1+ε	CARDINAL
ejpam-5621	310	1	j1	ORG
ejpam-5621	310	2	1+ε	CARDINAL
ejpam-5621	310	3	1+ε	CARDINAL
ejpam-5621	310	4	s∑ m=1	DATE
ejpam-5621	310	5	1+ε	CARDINAL
ejpam-5621	310	6	s∑ m=1	PERCENT
ejpam-5621	310	7	1+ε	CARDINAL
ejpam-5621	311	1	1+ε	CARDINAL
ejpam-5621	311	2	c̄3 = c̄3(n,	PERSON
ejpam-5621	311	3	1 +	CARDINAL
ejpam-5621	311	4	1+ε	CARDINAL
ejpam-5621	312	1	1+ε	CARDINAL
ejpam-5621	312	2	1/2	CARDINAL
ejpam-5621	312	3	s∑ m=1	DATE
ejpam-5621	312	4	1+ε	CARDINAL
ejpam-5621	313	1	1+ε	CARDINAL
ejpam-5621	313	2	s∑ m=1 |gm|(	PERCENT
ejpam-5621	313	3	1+ε	CARDINAL
ejpam-5621	315	1	5	CARDINAL
ejpam-5621	326	1	h. ibrahim et al	PERSON
ejpam-5621	327	1	j. pure	PERSON
ejpam-5621	327	2	18	CARDINAL
ejpam-5621	327	3	2	CARDINAL
ejpam-5621	327	4	2025	CARDINAL
ejpam-5621	327	5	5621 16	DATE
ejpam-5621	327	6	16	CARDINAL
ejpam-5621	328	1	1	CARDINAL
ejpam-5621	328	2	j. manfredi	PERSON
ejpam-5621	328	3	e. dibenedetto	PERSON
ejpam-5621	330	1	j. reine angew	PERSON
ejpam-5621	330	2	115:1107–1134, 1993	DATE
ejpam-5621	331	1	2	CARDINAL
ejpam-5621	333	1	75:293–312	CARDINAL
ejpam-5621	333	2	1983	DATE
ejpam-5621	334	1	3	CARDINAL
ejpam-5621	334	2	g. mingione	PERSON
ejpam-5621	336	1	j. reine angew	PERSON
ejpam-5621	336	2	2005	DATE
ejpam-5621	337	1	4	CARDINAL
ejpam-5621	337	2	k habib	PERSON
ejpam-5621	337	3	n saleem	PERSON
ejpam-5621	339	1	81	DATE
ejpam-5621	339	2	2024	DATE
ejpam-5621	340	1	5	CARDINAL
ejpam-5621	340	2	s. zhou j. kinnunen	PERSON
ejpam-5621	342	1	24:2043–2068, 1999	DATE
ejpam-5621	343	1	6	CARDINAL
ejpam-5621	343	2	g. mingione	PERSON
ejpam-5621	345	1	sci	ORG
ejpam-5621	345	2	276:15–36	DATE
ejpam-5621	345	3	2023	CARDINAL
ejpam-5621	346	1	7	CARDINAL
ejpam-5621	346	2	g. cupini	PERSON
ejpam-5621	346	3	e. mascolo	PERSON
ejpam-5621	348	1	und angewandte mathematik	PERSON
ejpam-5621	348	2	2005	DATE
ejpam-5621	349	1	8	CARDINAL
ejpam-5621	349	2	caifang wang	PERSON
ejpam-5621	351	1	j. math	PERSON
ejpam-5621	352	1	338:427–437, 2008	DATE
ejpam-5621	353	1	9	CARDINAL
ejpam-5621	353	2	f jarad	GPE
ejpam-5621	354	1	convergence	PERSON
ejpam-5621	355	1	2022:1–10, 2002	DATE
ejpam-5621	356	1	10	CARDINAL
ejpam-5621	356	2	l. wang	PERSON
ejpam-5621	357	1	reifenberg	GPE
ejpam-5621	359	1	57(10):1283	CARDINAL
ejpam-5621	359	2	1310, 2004	DATE
ejpam-5621	360	1	11	CARDINAL
ejpam-5621	360	2	l. wang	PERSON
ejpam-5621	361	1	reifenberg	GPE
ejpam-5621	365	1	176:271	DATE
ejpam-5621	365	2	301, 2005	DATE
ejpam-5621	366	1	12	CARDINAL
ejpam-5621	368	1	51(1):126–150	CARDINAL
ejpam-5621	368	2	1984	DATE
ejpam-5621	369	1	13	CARDINAL
ejpam-5621	369	2	y wei	PERSON
ejpam-5621	369	3	j zhang	PERSON
ejpam-5621	371	1	416(1):576	CARDINAL
ejpam-5621	371	2	613	CARDINAL
ejpam-5621	371	3	2025	DATE
ejpam-5621	372	1	14	CARDINAL
ejpam-5621	372	2	g. mingione	PERSON
ejpam-5621	375	1	j.	PERSON
ejpam-5621	375	2	136:285–320	DATE
ejpam-5621	375	3	2007	DATE
ejpam-5621	376	1	15	CARDINAL
ejpam-5621	376	2	y. chen	PERSON
ejpam-5621	376	3	l. wu	PERSON
ejpam-5621	378	1	amer	PERSON
ejpam-5621	379	1	j. math	PERSON
ejpam-5621	379	2	ri	GPE
ejpam-5621	379	3	1998	DATE
ejpam-5621	380	1	16	CARDINAL
ejpam-5621	380	2	m. giquinta	PERSON
ejpam-5621	382	1	princeton university press	ORG
ejpam-5621	382	2	princeton	GPE
ejpam-5621	382	3	nj	GPE
ejpam-5621	382	4	1983	DATE