Open Access
Translator Disclaimer
November 2016 Remarks on the strong maximum principle involving $p$-Laplacian
Xiaojing Liu, Toshio Horiuchi
Hiroshima Math. J. 46(3): 311-331 (November 2016). DOI: 10.32917/hmj/1487991624

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

Download 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

Information

Received: 13 July 2015; Revised: 20 May 2016; Published: November 2016
First available in Project Euclid: 25 February 2017

zbMATH: 1362.35062
MathSciNet: MR3614300
Digital Object Identifier: 10.32917/hmj/1487991624

Subjects:
Primary: 35B50
Secondary: 35J92

Rights: Copyright © 2016 Hiroshima University, Mathematics Program

JOURNAL ARTICLE
21 PAGES


SHARE
Vol.46 • No. 3 • November 2016
Back to Top