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

1 Dipartimento di Matematica, Politecnico di Milano, piazza Leonardo da Vinci 32, 20133 Milano,Italy
2 Dipartimento di Matematica ed Informatica, Universit`a di Palermo via Archirafi 34, 90123Palermo, Italy

In this paper we construct a viscosity solution of a two-phase free boundary problem for aclass of fully nonlinear equation with distributed sources, via an adaptation of the Perron method. Ourresults extend those in [Ca arelli, 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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Keywords Perron method; two-phase free boundary problems; fully nonlinear elliptic equations

Citation: Sandro Salsa, Francesco Tulone, Gianmaria Verzini. Existence of viscosity solutions to two-phase problems for fully nonlinear equations with distributed sources. Mathematics in Engineering, 2018, 1(1): 147-173. doi: 10.3934/Mine.2018.1.147

References

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