Published Paper

Inserted: 21 jul 2022
Last Updated: 5 jan 2024

Journal: Nonlinear Anal.
Year: 2022
Doi: https://doi.org/10.1016/j.na.2022.112966

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.

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• Piccinini_obstacle_arXiv.pdf