Sharp regularity estimates for quasilinear evolution equations

TL;DR

This paper proves precise regularity estimates for solutions of quasilinear evolution equations of p-Laplacian type, advancing understanding of their smoothness properties using geometric and intrinsic scaling techniques.

Contribution

It introduces a novel geometric tangential approach with oscillation mechanisms and intrinsic scaling to establish sharp $C^{1+eta}$ regularity for these equations.

Findings

Established sharp $C^{1+eta}$ regularity estimates for p-Laplacian evolution equations

Developed a geometric tangential method combined with oscillation control

Provided a systematic framework for regularity analysis in nonlinear evolution equations

Abstract

We establish sharp geometric $C^{1+\alpha}$ regularity estimates for bounded weak solutions of evolution equations of $p$-Laplacian type. Our approach is based on geometric tangential methods, and makes use of a systematic oscillation mechanism combined with an adjusted intrinsic scaling argument.