Fine boundary regularity for the degenerate fractional $p$-Laplacian

Antonio Iannizzotto; Sunra Mosconi; Marco Squassina

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arXiv · 1807.09497

Fine boundary regularity for the degenerate fractional $p$-Laplacian

Antonio Iannizzotto·Sunra Mosconi·Marco Squassina

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Abstract

We consider a pseudo-differential equation driven by the fractional $p$-Laplacian with $p\ge 2$ (degenerate case), with a bounded reaction $f$ and Dirichlet type conditions in a smooth domain $\Omega$. By means of barriers, a nonlocal superposition principle, and the comparison principle, we prove that any weak solution $u$ of such equation exhibits a weighted H\"older regularity up to the boundary, that is, $u/d^s\in C^\alpha(\overline\Omega)$ for some $\alpha\in(0,1)$, $d$ being the distance from the boundary.

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Antonio Iannizzotto, Sunra Mosconi, Marco Squassina. 2018-07-25. Fine boundary regularity for the degenerate fractional $p$-Laplacian. https://arxiv.org/abs/1807.09497

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