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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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 |