${{W}^{2,δ}}$ Estimates for Solution Sets of Fully Nonlinear Elliptic inequalities on ${C^{1,α}}$ Domains

In this paper, we establish boundary $W^{2,δ}$ estimates for $u\in S(λ,Λ,f)$ on $C^{1,α}$ domains with $f\in L^p$ as $n<p<\infty$ and $C^{1,α}$ boundary values. Instead of straightening out the boundary, our main idea is to obtain boundary $W^{2,δ}$ estimates from interior $W^{2,δ_0}$ estimates and Whitney decomposition for some $δ\leq δ_0$.

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