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arXiv · 2508.17875

A new proof of H\"older estimates for the gradient of quasilinear elliptic equations

Dongsheng Li·Yasheng Lyu
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Abstract

In this paper, we give a new proof of H\"older 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, H\"older estimates for the gradient of fully nonlinear elliptic equations are also obtained by the same method.

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Dongsheng Li, Yasheng Lyu. 2025-08-25. A new proof of H\"older estimates for the gradient of quasilinear elliptic equations. https://arxiv.org/abs/2508.17875

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