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

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 $\delta \le {\delta }_0$.

9 pages. arXiv admin note: text overlap with arXiv:2201.01975