id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejde-1276	Kim, Yong-Cheol	Holder regularity of weak solutions to nonlocal p-Laplacian type Schrodinger  equations with A_1^p-Muckenhoupt potentials	2025	26	.pdf	application/pdf	12738	649	86	(2.8) EJDE-2025/83 HÖLDER REGULARITY OF WEAK SOLUTIONS 7 For g ∈ W s,p(Rn), we consider the convex subsets of Xs,p(Ω) defined by Xs,p g (Ω)± = {v ∈ Xs,p(Ω) : (g − v)± ∈ Xs,p 0 (Ω)}, Xs,p g (Ω) := Xs,p g (Ω)+ ∩Xs,p g (Ω)− = {v ∈ Xs,p(Ω) : g − v ∈ Xs,p 0 (Ω)}. If the nonlocal equation mentioned just in the above is considered for 0 < s < 1, p ≥ 2 and a bounded domain Ω ⊂ Rn with C1,1 boundary, then they also established the first fine boundary regularity for its weak solutions in [18], i.e. there exist some α ∈ (0, s] and C > 0 depending only on n, p, s and Ω such that∥∥∥ u dsΩ ∥∥∥ Cα(Ω) ≤ C∥f∥ 1 p−1 L∞(Ω) for any weak solution u ∈ W s,p 0 (Ω) of the nonlocal equation, where dΩ(x) = dist(x, ∂Ω).	cache/ejde-1276.pdf	txt/ejde-1276.txt