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

Bin Shang; Chao Zhang

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arXiv · 2112.08698

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

Bin Shang·Chao Zhang

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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.

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Bin Shang, Chao Zhang. 2021-12-16. H\"{o}lder regularity for mixed local and nonlocal $p$-Laplace parabolic equations. https://arxiv.org/abs/2112.08698

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