Calculus of Variations and Geometric Measure Theory

M. Piccinini

The obstacle problem and the Perron Method for nonlinear fractional equations in the Heisenberg group

created by piccinini on 21 Jul 2022
modified on 28 Jul 2022


Published Paper

Inserted: 21 jul 2022
Last Updated: 28 jul 2022

Journal: Nonlinear Anal.
Year: 2022

ArXiv: 2207.03743 PDF


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.