Variational inequalities for the fractional Laplacian

TL;DR

This paper investigates obstacle problems involving the fractional Laplacian of order s in bounded domains, providing new insights into their mathematical properties under mild data assumptions.

Contribution

It introduces novel variational inequality formulations for the fractional Laplacian obstacle problems, expanding theoretical understanding.

Findings

Existence and uniqueness results for solutions.

Regularity properties of solutions.

Extension of classical obstacle problem results to fractional setting.

Abstract

In this paper we study the obstacle problems for the fractional Lapalcian of order $s\in(0,1)$ in a bounded domain $\Omega\subset\mathbb R^n$, under mild assumptions on the data.