Sub-solutions and a point-wise Hopf's Lemma for Fractional p-Laplacian

Zaizheng Li; Qidi Zhang

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arXiv · 1905.00127

Sub-solutions and a point-wise Hopf's Lemma for Fractional p-Laplacian

Zaizheng Li·Qidi Zhang

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Abstract

We prove a Hopf's lemma in the point-wise sense. The essential technique is to prove $(-Δ)^s_p u(x)$ is uniformly bounded in the unit ball $B_1\subset\mathbb{R}^n$, where $u(x)=(1-|x|^2)^s_{+}$. Also we study the global Hölder continuity of bounded positive solutions for $(-Δ)^s_p u(x)=f(x,u).$

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BibTeX RIS

Zaizheng Li, Qidi Zhang. 2020-06-23. Sub-solutions and a point-wise Hopf's Lemma for Fractional p-Laplacian. https://arxiv.org/abs/1905.00127

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