The obstacle problem for nonlinear integro-differential operators
Analysis of PDEs
2016-04-18 v1
Abstract
We investigate the obstacle problem for a class of nonlinear equations driven by nonlocal, possibly degenerate, integro-differential operators, whose model is the fractional -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.
Cite
@article{arxiv.1604.04521,
title = {The obstacle problem for nonlinear integro-differential operators},
author = {Janne Korvenpaa and Tuomo Kuusi and Giampiero Palatucci},
journal= {arXiv preprint arXiv:1604.04521},
year = {2016}
}
Comments
to appear in Calc. Var. Partial Differential Equations