# Continuity results with respect to domain perturbation for the fractional $p-$laplacian

## TL;DR

This paper establishes conditions based on fractional capacity under which solutions to the fractional p-Laplacian remain continuous when the domain is perturbed, advancing understanding of domain stability in fractional PDEs.

## Contribution

It introduces fractional capacity-based criteria ensuring solution continuity for the fractional p-Laplacian under domain perturbations.

## Key findings

- Solutions are continuous under fractional capacity conditions.
- Provides sufficient criteria for domain approximation stability.
- Enhances understanding of fractional PDEs in variable domains.

## Abstract

In this paper we give sufficient conditions on the approximating domains in order to obtain the continuity of solutions for the fractional $p-$laplacian. These conditions are given in terms of the fractional capacity of the approximating domains.