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Pointwise Regularity for Fully Nonlinear Elliptic Equations in General Forms by Lian, Yuanyuan; Wang, Lihe; Zhang, Kai is a scholarly article available to read on EtoBox.

What is Pointwise Regularity for Fully Nonlinear Elliptic Equations in General Forms about?

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 ($k\geq 1$ and $0<\alpha<1$). In addition, we also derive the pointwise $C^k$ regularity ($k\geq 1$) and $C^{k,\mathrm{lnL}}$ regularity ($k\geq 0$), 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.

Author

Lian, Yuanyuan; Wang, Lihe; Zhang, Kai

Published

2020

Language

EN