A new proof of Hölder estimates for the gradient of quasilinear elliptic equations

2025/08/25 by Li, Dongsheng, Lyu, Yasheng
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.17875

Abstract

In this paper, we give a new proof of Hölder estimates for the gradient of quasilinear elliptic equations, using a covering method inspired by the proof of Evans-Krylov theorem for fully nonlinear elliptic equations. Moreover, Hölder estimates for the gradient of fully nonlinear elliptic equations are also obtained by the same method.

Citations

• The Evans-Krylov theorem for non local fully non linear equations
• The Evans-Krylov theorem for nonlocal fully nonlinear equations
• On the Evans-Krylov theorem

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