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arXiv · 2201.02951

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

Dongsheng Li·Xuemei Li
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Abstract

In this paper, we establish boundary $W^{2,\delta}$ estimates for $u\in S(\lambda,\Lambda,f)$ on $C^{1,\alpha}$ domains with $f\in L^p$ as $n<p<\infty$ and $C^{1,\alpha}$ boundary values. Instead of straightening out the boundary, our main idea is to obtain boundary $W^{2,\delta}$ estimates from interior $W^{2,\delta_0}$ estimates and Whitney decomposition for some $\delta\leq \delta_0$.

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Dongsheng Li, Xuemei Li. 2022-01-09. ${{W}^{2,\delta}}$ Estimates for Solution Sets of Fully Nonlinear Elliptic inequalities on ${C^{1,\alpha}}$ Domains. https://arxiv.org/abs/2201.02951

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