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Abstract

We establish a strong maximum principle for weak solutions of the mixed local and nonlocal p-Laplace equation $\begin{array}{l} - Δ_{p} u + {(- Δ)}_{p}^{s} u = c (x) | u |^{p - 2} u in Ω, \end{array}$ where $Ω \subset R^{N}$ is an open set, $p \in (1, \infty)$ , $s \in (0, 1)$ and $c \in C (\overline{Ω})$ .

Keywords

Strong maximum principle weak solutions viscosity solutions

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A strong maximum principle for mixed local and nonlocal p -Laplace equations

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