On a two-phase free boundary problem ruled by the infinity Laplacian

Damião J. Araújo, Eduardo V. Teixeira, José Miguel Urbano

Research output: Contribution to journalArticlepeer-review

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Abstract

In this paper we consider a two-phase free boundary problem ruled by the infinity Laplacian. Our main result states that bounded viscosity solutions in B1 are universally Lipschitz continuous in B1/2, which is the optimal regularity for the problem. We make a new use of the Ishii–Lions’ method, which works as a surrogate for the lack of a monotonicity formula and is bound to be applicable in related problems.
Original languageEnglish (US)
Pages (from-to)773-785
Number of pages13
JournalIsrael Journal of Mathematics
Volume245
Issue number2
DOIs
StatePublished - Oct 1 2021
Externally publishedYes

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