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Existence of viscosity solutions to two-phase problems for fully nonlinear equations with distributed sources

Sandro Salsa Francesco Tulone Gianmaria Verzini

*Corresponding author: Gianmaria Verzini gianmaria.verzini@polimi.it.

MinE2019,1,147doi:10.3934/Mine.2018.1.147

In this paper we construct a viscosity solution of a two-phase free boundary problem for a class of fully nonlinear equation with distributed sources, via an adaptation of the Perron method. Our results extend those in [Caffarelli, 1988], [Wang, 2003] for the homogeneous case, and of [De Silva, Ferrari, Salsa, 2015] for divergence form operators with right hand side.

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