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.
Salsa, S., Tulone, F., Verzini, G. (2018). Existence of viscosity solutions to two-phase problems for fully nonlinear equations with distributed sources. MATHEMATICS IN ENGINEERING, 1(1), 147-173 [10.3934/Mine.2018.1.147].
Existence of viscosity solutions to two-phase problems for fully nonlinear equations with distributed sources
Tulone, Francesco
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2018-01-01
Abstract
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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