Singularly perturbed fully nonlinear parabolic problems and their asymptotic free boundaries

Gleydson C. Ricarte; Rafayel Teymurazyan; José Miguel Urbano

doi:10.4171/rmi/1091

Singularly perturbed fully nonlinear parabolic problems and their asymptotic free boundaries

Gleydson C. Ricarte, Rafayel Teymurazyan, José Miguel Urbano

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We study fully nonlinear singularly perturbed parabolic equations and their limits. We show that solutions are uniformly Lipschitz continuous in space and Hölder continuous in time. For the limiting free boundary problem, we analyse the behaviour of solutions near the free boundary. We show, in particular, that, at each time level, the free boundary is a porous set and, consequently, is of Lebesgue measure zero. For rotationally invariant operators, we also derive the limiting free boundary condition.

Original language	English (US)
Pages (from-to)	1535-1558
Number of pages	24
Journal	Revista Matematica Iberoamericana
Volume	35
Issue number	5
DOIs	https://doi.org/10.4171/rmi/1091
State	Published - Jan 1 2019
Externally published	Yes

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Generated from Scopus record by KAUST IRTS on 2023-02-15

ASJC Scopus subject areas

General Mathematics

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abstract = "We study fully nonlinear singularly perturbed parabolic equations and their limits. We show that solutions are uniformly Lipschitz continuous in space and H{\"o}lder continuous in time. For the limiting free boundary problem, we analyse the behaviour of solutions near the free boundary. We show, in particular, that, at each time level, the free boundary is a porous set and, consequently, is of Lebesgue measure zero. For rotationally invariant operators, we also derive the limiting free boundary condition.",

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AU - Ricarte, Gleydson C.

AU - Teymurazyan, Rafayel

AU - Urbano, José Miguel

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PY - 2019/1/1

Y1 - 2019/1/1

N2 - We study fully nonlinear singularly perturbed parabolic equations and their limits. We show that solutions are uniformly Lipschitz continuous in space and Hölder continuous in time. For the limiting free boundary problem, we analyse the behaviour of solutions near the free boundary. We show, in particular, that, at each time level, the free boundary is a porous set and, consequently, is of Lebesgue measure zero. For rotationally invariant operators, we also derive the limiting free boundary condition.

AB - We study fully nonlinear singularly perturbed parabolic equations and their limits. We show that solutions are uniformly Lipschitz continuous in space and Hölder continuous in time. For the limiting free boundary problem, we analyse the behaviour of solutions near the free boundary. We show, in particular, that, at each time level, the free boundary is a porous set and, consequently, is of Lebesgue measure zero. For rotationally invariant operators, we also derive the limiting free boundary condition.

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Singularly perturbed fully nonlinear parabolic problems and their asymptotic free boundaries

Abstract

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