Fractional elliptic problems with nonlinear gradient sources and measures

DA SILVA, JOÃO VITOR; PABLO OCHOA; ANALÍA SILVA

REVISTA MATEMATICA COMPLUTENSE

UNIV COMPLUTENSE MADRID

Lugar: Obsrvación: La editorial es Springer y no UCM; Año: 2021

1139-1138

In this manuscript we deal with existence/uniqueness and regularity issues of suitableweak solutions to nonlocal problems driven by fractional Laplace type operators. Differentfrom previous researches, in our approach we consider gradient non-linearity sources with subcriticalgrowth, as well as appropriated measures as sources and boundary datum. We providean in-depth discussion on the notions of solutions involved together with existence/uniquenessresults in different regimes and for different boundary value problems. Finally, this work extendsprevious ones by dealing with more general nonlocal operators, source terms and boundary data.