Variational inequalities for the spectral fractional Laplacian

TL;DR

This paper investigates obstacle problems involving the spectral fractional Laplacian in bounded domains, focusing on variational inequalities and their mathematical properties.

Contribution

It introduces a framework for analyzing obstacle problems for the spectral fractional Laplacian, extending existing theories to fractional orders in bounded domains.

Findings

Established existence and uniqueness of solutions

Derived regularity properties of solutions

Provided new variational inequality formulations

Abstract

In this paper we study the obstacle problems for the Navier (spectral) fractional Laplacian $\left(-\Delta_\Omega\right)^{\!s}$ of order $s\in(0,1)$, in a bounded domain $\Omega\subset\mathbb R^n$.