The obstacle problem and the Perron Method for nonlinear fractional equations in the Heisenberg group
Analysis of PDEs
2023-01-12 v2
Abstract
We study the obstacle problem related to a wide class of nonlinear integro-differential operators, whose model is the fractional subLaplacian in the Heisenberg group. We prove both the existence and uniqueness of the solution, and that solutions inherit regularity properties of the obstacle such as boundedness, continuity and H\"older continuity up to the boundary. We also prove some independent properties of weak supersolutions to the class of problems we are dealing with. Armed with the aforementioned results, we finally investigate the Perron-Wiener-Brelot generalized solution by proving its existence for very general boundary data.
Keywords
Cite
@article{arxiv.2207.03743,
title = {The obstacle problem and the Perron Method for nonlinear fractional equations in the Heisenberg group},
author = {Mirco Piccinini},
journal= {arXiv preprint arXiv:2207.03743},
year = {2023}
}
Comments
We have removed the bound on the integrability exponent p. To appear in Nonlinear Anal