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- W4383722140 abstract "In this paper, we study the boundary regularity for viscosity solutions of fully nonlinear elliptic equations. We use a unified, simple method to prove that if the domain $Omega$ satisfies the exterior $C^{1,mathrm{Dini}}$ condition at $x_0in partial Omega$ (see Definition 1.2), the solution is Lipschitz continuous at $x_0$; if $Omega$ satisfies the interior $C^{1,mathrm{Dini}}$ condition at $x_0$ (see Definition 1.3), the Hopf lemma holds at $x_0$. The key idea is that the curved boundaries are regarded as perturbations of a hyperplane. Moreover, we show that the $C^{1,mathrm{Dini}}$ conditions are optimal." @default.
- W4383722140 created "2023-07-11" @default.
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- W4383722140 date "2023-07-10" @default.
- W4383722140 modified "2023-09-26" @default.
- W4383722140 title "Boundary Lipschitz Regularity and the Hopf Lemma for Fully Nonlinear Elliptic Equations" @default.
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- W4383722140 doi "https://doi.org/10.1007/s11118-023-10085-6" @default.
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