Calculus of Variations and Geometric Measure Theory

J. Korvenpaa - T. Kuusi - G. Palatucci

Hölder continuity up to the boundary for a class of fractional obstacle problems

created by palatucci on 26 Mar 2016
modified on 18 May 2016


Published Paper

Inserted: 26 mar 2016
Last Updated: 18 may 2016

Journal: Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl.
Volume: 27
Pages: 355--367
Year: 2016
Doi: 10.4171/RLM/739


We deal with the obstacle problem for a class of nonlinear integro-differential operators, whose model is the fractional $p$-Laplacian with measurable coefficients. In accordance with well-known results for the analog for the pure fractional Laplacian operator, the corresponding solutions inherit regularity properties from the obstacle, both in the case of boundedness, continuity, and Hölder continuity, up to the boundary.

Keywords: obstacle problem, fractional Sobolev spaces, quasilinear nonlocal operators, Caccioppoli estimates, nonlocal tail