Fractional elliptic problems with nonlinear gradient sources and measures
Analysis of PDEs
2020-05-28 v2
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.
Cite
@article{arxiv.1906.02804,
title = {Fractional elliptic problems with nonlinear gradient sources and measures},
author = {João Vitor da Silva and Pablo Ochoa and Analía Silva},
journal= {arXiv preprint arXiv:1906.02804},
year = {2020}
}