H\"{o}lder regularity for mixed local and nonlocal $p$-Laplace parabolic equations

TL;DR

This paper proves H"older regularity for solutions to mixed local and nonlocal p-Laplace parabolic equations across all exponents, using energy estimates and positivity expansion techniques.

Contribution

It provides a unified proof of regularity for a broad class of mixed local and nonlocal p-Laplace equations, covering the full range of exponents.

Findings

H"older regularity established for all p in (1, ∞)

Unified proof method applicable to mixed local and nonlocal equations

Utilizes energy estimates and De Giorgi type lemmas

Abstract

We give a unified proof of H\"{o}lder regularity of weak solutions for mixed local and nonlocal $p$-Laplace type parabolic equations with the full range of exponents $1<p<\infty$. Our proof is based on the expansion of positivity together with the energy estimate and De Giorgi type lemma.