Boundary differentiability of infinity harmonic functions. (English) Zbl 1284.35100
Summary: We prove that an infinity harmonic function \(u(x)\in C({\overline\varOmega})\) is differentiable at a boundary point \(x_0\in \partial {\varOmega}\) if both \(\partial{\varOmega}\) and the boundary data \(g(x)\) are differentiable at \(x_0\). This work improved a former result of C. Wang and Y. Yu [Math. Res. Lett. 19, No. 4, 823–835 (2012; Zbl 1270.35233)]. They obtained the boundary differentiability of \(u(x)\) with the \(C^1\) assumption on \(\partial{\varOmega}\) and \(g(x)\).
MSC:
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 35J67 | Boundary values of solutions to elliptic equations and elliptic systems |
Keywords:
infinity harmonic functions; boundary differentiability; differentiable boundary; differentiable boundary dataCitations:
Zbl 1270.35233References:
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