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

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, Ferr...

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Main Authors:	Sandro Salsa, Francesco Tulone, Gianmaria Verzini
Format:	Article
Language:	English
Published:	AIMS Press 2018-10-01
Series:	Mathematics in Engineering
Subjects:	Perron method\| two-phase free boundary problems\| fully nonlinear elliptic equations
Online Access:	https://www.aimspress.com/article/10.3934/Mine.2018.1.147/fulltext.html

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spelling	doaj-2d7c46795ca64af68c39c1db9e585a602020-11-25T02:34:04ZengAIMS PressMathematics in Engineering2640-35012018-10-011114717310.3934/Mine.2018.1.147Existence of viscosity solutions to two-phase problems for fully nonlinear equations with distributed sourcesSandro Salsa0Francesco Tulone1Gianmaria Verzini21 Dipartimento di Matematica, Politecnico di Milano, piazza Leonardo da Vinci 32, 20133 Milano,Italy2 Dipartimento di Matematica ed Informatica, Università di Palermo via Archirafi 34, 90123 Palermo, Italy1 Dipartimento di Matematica, Politecnico di Milano, piazza Leonardo da Vinci 32, 20133 Milano,ItalyIn 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.https://www.aimspress.com/article/10.3934/Mine.2018.1.147/fulltext.htmlPerron method\| two-phase free boundary problems\| fully nonlinear elliptic equations
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Sandro Salsa Francesco Tulone Gianmaria Verzini
spellingShingle	Sandro Salsa Francesco Tulone Gianmaria Verzini Existence of viscosity solutions to two-phase problems for fully nonlinear equations with distributed sources Mathematics in Engineering Perron method\| two-phase free boundary problems\| fully nonlinear elliptic equations
author_facet	Sandro Salsa Francesco Tulone Gianmaria Verzini
author_sort	Sandro Salsa
title	Existence of viscosity solutions to two-phase problems for fully nonlinear equations with distributed sources
title_short	Existence of viscosity solutions to two-phase problems for fully nonlinear equations with distributed sources
title_full	Existence of viscosity solutions to two-phase problems for fully nonlinear equations with distributed sources
title_fullStr	Existence of viscosity solutions to two-phase problems for fully nonlinear equations with distributed sources
title_full_unstemmed	Existence of viscosity solutions to two-phase problems for fully nonlinear equations with distributed sources
title_sort	existence of viscosity solutions to two-phase problems for fully nonlinear equations with distributed sources
publisher	AIMS Press
series	Mathematics in Engineering
issn	2640-3501
publishDate	2018-10-01
description	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.
topic	Perron method\| two-phase free boundary problems\| fully nonlinear elliptic equations
url	https://www.aimspress.com/article/10.3934/Mine.2018.1.147/fulltext.html
work_keys_str_mv	AT sandrosalsa existenceofviscositysolutionstotwophaseproblemsforfullynonlinearequationswithdistributedsources AT francescotulone existenceofviscositysolutionstotwophaseproblemsforfullynonlinearequationswithdistributedsources AT gianmariaverzini existenceofviscositysolutionstotwophaseproblemsforfullynonlinearequationswithdistributedsources
_version_	1724810336474759168

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

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