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...

Full description

Bibliographic Details
Main Authors: Sandro Salsa, Francesco Tulone, Gianmaria Verzini
Format: Article
Language:English
Published: AIMS Press 2018-10-01
Series:Mathematics in Engineering
Subjects:
Online Access:https://www.aimspress.com/article/10.3934/Mine.2018.1.147/fulltext.html
id doaj-2d7c46795ca64af68c39c1db9e585a60
record_format Article
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