6533b825fe1ef96bd1282915

RESEARCH PRODUCT

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

Sandro SalsaGianmaria VerziniGianmaria VerziniFrancesco Tulone

subject

Class (set theory)lcsh:T57-57.97Applied MathematicsPhase (waves)Perron methodfully nonlinear elliptic equationsPerron method| two-phase free boundary problems| fully nonlinear elliptic equationstwo-phase free boundary problemsNonlinear systemSettore MAT/05 - Analisi MatematicaViscosity (programming)lcsh:Applied mathematics. Quantitative methodsFree boundary problemApplied mathematicsViscosity solutionDivergence (statistics)Perron methodMathematical PhysicsAnalysisMathematics

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.

yearjournalcountryeditionlanguage
2018-10-01Mathematics in Engineering
https://doi.org/10.3934/mine.2018.1.147