Abstract
Let $N\ge 1, 1 \lt p \lt \infty$ and $p^*=\max(1,p-1)$. Let $\Omega$ be a bounded domain of $\mathbf{R}^N$. We establish the strong maximum principle for the $p$-Laplace operator with a nonlinear potential term. More precisely, we show that every super-solution $u \in \Omega^{1, p^*}_{\mathrm{loc}}(\Omega)$ vanishes identically in $\Omega$, if $u$ is admissible and $u = 0$ a.e on a set of positive $p$-capacity relative to $\Omega$.
Citation
Xiaojing Liu. Toshio Horiuchi. "Remarks on the strong maximum principle involving $p$-Laplacian." Hiroshima Math. J. 46 (3) 311 - 331, November 2016. https://doi.org/10.32917/hmj/1487991624
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