Calculus of Variations and Geometric Measure Theory

J. Korvenpaa - T. Kuusi - G. Palatucci

The obstacle problem for nonlinear integro-differential operators

created by palatucci on 18 Dec 2015
modified on 31 Aug 2016


Published Paper

Inserted: 18 dec 2015
Last Updated: 31 aug 2016

Journal: Calc. Var. Partial Differential Equations
Volume: 55
Number: 3
Pages: Art. 63
Year: 2016
Doi: 10.1007/s00526-016-0999-2


We investigate the obstacle problem for a class of nonlinear equations driven by nonlocal, possibly degenerate, integro-differential operators, whose model is the fractional $p$-Laplacian operator with measurable coefficients. Amongst other results, we will prove both the existence and uniqueness of the solutions to the obstacle problem, and that these solutions inherit regularity properties, such as boundedness, continuity and H\"older continuity (up to the boundary), from the obstacle.

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