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

Sandro Salsa; Francesco Tulone; Gianmaria Verzini; Sandro Salsa; Francesco Tulone; Gianmaria Verzini

doi:10.3934/Mine.2018.1.147

Mathematics in Engineering

2019, Volume 1, Issue 1: 147-173. doi: 10.3934/Mine.2018.1.147

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Research article

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, Università di Palermo via Archirafi 34, 90123 Palermo, Italy

Received: 16 July 2018 Accepted: 22 October 2018 Published: 25 October 2018

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 [Ca arelli, 1988], [Wang, 2003] for the homogeneous case, and of [De Silva, Ferrari, Salsa, 2015] for divergence form operators with right hand side.
- 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[J]. Mathematics in Engineering, 2019, 1(1): 147-173. doi: 10.3934/Mine.2018.1.147

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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 [Ca arelli, 1988], [Wang, 2003] for the homogeneous case, and of [De Silva, Ferrari, Salsa, 2015] for divergence form operators with right hand side.

References

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