Fractional elliptic problems with nonlinear gradient sources and measures

JOAO VITOR DA SILVA; ANALIA SILVA; PABLO OCHOA

REVISTA MATEMATICA COMPLUTENSE

UNIV COMPLUTENSE MADRID

Año: 2021 p. 1 - 30

1139-1138

In this manuscript we deal with existence/uniqueness and regularity issues of suit- able 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 sub- critical 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.