# Fractional elliptic problems with nonlinear gradient sources and measures

## TL;DR

This paper investigates the existence, uniqueness, and regularity of weak solutions to fractional elliptic problems with nonlinear gradient sources and measures, extending previous work to more general operators and data.

## Contribution

It introduces new results on solutions for nonlocal fractional problems with nonlinear gradient sources and measures, broadening the scope of prior research.

## Key findings

- Established existence and uniqueness results for various boundary value problems.
- Analyzed regularity properties of solutions under different conditions.
- Extended the framework to more general nonlocal operators and source terms.

## Abstract

In this manuscript we deal with existence/uniqueness and regularity issues of suitable weak solutions to nonlocal problems driven by fractional Laplace type operators. Different from previous researches, in our approach we consider gradient non-linearity sources with subcritical growth, as well as appropriated measures as sources and boundary datum. We provide an in-depth discussion on the notions of solutions involved together with existence/uniqueness results in different regimes and for different boundary value problems. Finally, this work extends previous ones by dealing with more general nonlocal operators, source terms and boundary data.