id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-1227	Antonio, Edgar; Arciga-Alejandre, Martin P.; Pardo, Rosa; Sanchez-Ortiz, Jorge	Uniform estimates for elliptic equations with Caratheodory nonlinearities at the interior and on the boundary	2025	15	.pdf	application/pdf	7493	380	80	Choosing, as before, sB , tB < qB , so that qBsB = rB , and tBs ′ B = 2∗ 2∗,N/rB −1 ; thus, tB := 2∗ 2∗,N/rB − 1 ( 1− qB rB ) < qB ⇐⇒ 1 qB − 1 rB < 2∗,N/rB − 1 2∗ = 1− 1 rB − N − 2 2(N − 1) ⇐⇒ 1 qB < N 2(N − 1) ⇐⇒ qB > 2(N − 1) N , (3.14) and the last inequality is satisfied since qB > N − 1 and N > 2. N − 2 = (N − 1) N 2∗, (2.2) are the critical Sobolev exponent and the critical exponent in the sense of the trace, respectively.	cache/ejde-1227.pdf	txt/ejde-1227.txt