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Regularity theory for mixed local and nonlocal parabolic p-Laplace equations (2107.09825v1)

Published 21 Jul 2021 in math.AP

Abstract: We investigate the mixed local and nonlocal parabolic $p$-Laplace equation \begin{align*} \partial_t u(x,t)-\Delta_p u(x,t)+\mathcal{L}u(x,t)=0, \end{align*} where $\Delta_p$ is the local $p$-Laplace operator and $\mathcal{L}$ is the nonlocal $p$-Laplace operator. Based on the combination of suitable Caccioppoli-type inequality and Logarithmic Lemma with a De Giorgi-Nash-Moser iteration, we establish the local boundedness and H\"{o}lder continuity of weak solutions for such equations.

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