Fractional elliptic problems with nonlinear gradient sources and measures

João Vitor da Silva; Pablo Ochoa; Analía Silva

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arXiv · 1906.02804

Fractional elliptic problems with nonlinear gradient sources and measures

João Vitor da Silva·Pablo Ochoa·Analía Silva

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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.

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BibTeX RIS

João Vitor da Silva, Pablo Ochoa, Analía Silva. 2020-05-26. Fractional elliptic problems with nonlinear gradient sources and measures. https://arxiv.org/abs/1906.02804

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