# Fractional order elliptic problems with inhomogeneous Dirichlet boundary conditions

## TL;DR

This paper studies fractional-order elliptic problems with inhomogeneous boundary conditions, proposing a boundary integral model and analyzing the potential operators to establish solution existence.

## Contribution

It introduces a boundary integral formulation for fractional elliptic problems with inhomogeneous Dirichlet data and refines the associated potential operator theory.

## Key findings

- Established mapping properties of potential operators
- Provided conditions for classical solution existence
- Proposed a boundary integral model for fractional elliptic problems

## Abstract

Fractional-order elliptic problems are investigated in case of inhomogeneous Dirichlet boundary data. The boundary integral form is proposed as a suitable mathematical model. The corresponding theory is completed by sharpening the mapping properties of the corresponding potential operators. Also a mild condition is provided to ensure the existence of the classical solution of the boundary integral equation.