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- W3107716191 abstract "In this paper, we develop systematically the pointwise regularity for viscosity solutions of fully nonlinear elliptic equations in general forms. In particular, the equations with quadratic growth (called natural growth) in the gradient are covered. We obtain a series of interior and boundary pointwise $C^{k,alpha}$ regularity ($kgeq 1$ and $0<alpha<1$). In addition, we also derive the pointwise $C^k$ regularity ($kgeq 1$) and $C^{k,mathrm{lnL}}$ regularity ($kgeq 0$), which correspond to the end points $alpha=0$ and $alpha=1$ respectively. Some regularity results are new even for the linear equations. Moreover, the minimum requirements are imposed to obtain above regularity and our proofs are simple." @default.
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- W3107716191 date "2020-12-01" @default.
- W3107716191 modified "2023-10-18" @default.
- W3107716191 title "Pointwise Regularity for Fully Nonlinear Elliptic Equations in General Forms" @default.
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- W3107716191 doi "https://doi.org/10.48550/arxiv.2012.00324" @default.
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