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arXiv · 1907.08814

Sobolev versus Hölder minimizers for the degenerate fractional $p$-Laplacian

Antonio Iannizzotto·Sunra Mosconi·Marco Squassina
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Abstract

We consider a nonlinear pseudo-differential equation driven by the fractional $p$-Laplacian $(-Δ)^s_p$ with $s\in(0,1)$ and $p\ge 2$ (degenerate case), under Dirichlet type conditions in a smooth domain $Ω$. We prove that local minimizers of the associated energy functional in the fractional Sobolev space $W^{s,p}_0(Ω)$ and in the weighted Hölder space $C^0_s(\overlineΩ)$, respectively, do coincide.

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Antonio Iannizzotto, Sunra Mosconi, Marco Squassina. 2019-07-20. Sobolev versus Hölder minimizers for the degenerate fractional $p$-Laplacian. https://arxiv.org/abs/1907.08814

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