Calculus of Variations and Geometric Measure Theory

A. Iannizzotto - S. J. N. Mosconi - M. Squassina

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

created by squassina on 20 Jul 2019



Inserted: 20 jul 2019
Last Updated: 20 jul 2019

Year: 2019


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