Antimaximum principle in exterior domains

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• 作者：T.V. Anoop^a ; ^{anoop@iitm.ac.in" class="auth_mail" title="E-mail the corresponding author} ; P. Drá ; bek^b ; ^{pdrabek@kma.zcu.cz" class="auth_mail" title="E-mail the corresponding author} ; Lakshmi Sankar^c ; ^{lakshmi@niser.ac.in" class="auth_mail" title="E-mail the corresponding author} ; Sarath Sasi^c ; ^{sarath@niser.ac.in" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35J92 ; 35P30 ; 35B05
• 刊名：Nonlinear Analysis
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：130
• 期：Complete
• 页码：241-254
• 全文大小：684 K

文摘

We consider the antimaximum principle for the p$p$-Laplacian in the exterior domain: where Δ_p${\Delta }_p$ is the p$p$-Laplace operator with p>1$p>1$,λ$\lambda$ is the spectral parameter and $B_1^c$ is the exterior of the closed unit ball in 356da0aad184e6950af13bac37f6533" title="Click to view the MathML source">R^N${\mathbb{R}}^N$ with N≥1$N\ge 1$. The function h$h$ is assumed to be nonnegative and nonzero, however the weight function K$K$ is allowed to change its sign. For K$K$ in a certain weighted Lebesgue space, we prove that the antimaximum principle holds locally. A global antimaximum principle is obtained for h$h$ with compact support. For a compactly supported K$K$, with N=1$N=1$ and p=2$p=2$, we provide a necessary and sufficient condition on h$h$ for the global antimaximum principle. In the course of proving our results we also establish the boundary regularity of solutions of certain boundary value problems.