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arXiv · 1901.06065

Pointwise Boundary Differentiability of Solutions of Elliptic Equations

Yongpan Huang·Dongsheng Li·Kai Zhang
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Abstract

In this paper, we give pointwise geometric conditions on the boundary which guarantee the differentiability of the solution at the boundary. Precisely, the geometric conditions are two parts: the proper blow up condition (see Definition 1) and the exterior Dini hypersurface condition (see Definition 2). If $\Omega$ satisfies this two conditions at $x_0\in\partial \Omega$, the solution is differentiable at $x_0$. Furthermore, counterexamples show that the conditions are optimal (see Remark 3 and the counterexample in Section 2).

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Yongpan Huang, Dongsheng Li, Kai Zhang. 2019-01-18. Pointwise Boundary Differentiability of Solutions of Elliptic Equations. https://doi.org/10.1007/s00229-016-0850-2

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