Research article

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

  • 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.

    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

    Related Papers:

  • 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.


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