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

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.

Publication Details

Journal
ArXiv.org
Published
2025-08-25
Primary Topic
Geochemistry and Geologic Mapping
Type
article
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article

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

ArXiv.org
Geochemistry and Geologic Mapping
article

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

article en

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.

ArXiv.org
Openalex Percentile: Top 64%
Geochemistry and Geologic Mapping
Open Access PDFOpenAlex
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A new proof of Hölder estimates for the gradient of quasilinear elliptic equations · ArXiv.org (2025) | TGRS Research Map | TGRS