Inverse problems for the spectral fractional Laplacian with inhomogeneous Dirichlet boundary data

TL;DR

This paper investigates inverse problems related to the spectral fractional Laplacian with inhomogeneous boundary data, introducing a Dirichlet-to-Neumann map and proving a density result.

Contribution

It introduces a Dirichlet-to-Neumann map for the spectral fractional Laplacian and analyzes an associated inverse problem, along with establishing a density result.

Findings

Defined a Dirichlet-to-Neumann map for the spectral fractional Laplacian

Analyzed the inverse problem related to this operator

Proved a density result for the spectral fractional Laplacian

Abstract

In this paper, we study the spectral fractional Laplacian with inhomogeneous Dirichlet boundary data. Our contributions are twofold: first we introduce a Dirichlet-to-Neumann map for this operator and analyze an associated inverse problem; and second we establish an additional density result for the spectral fractional Laplacian.