Regularity for the two phase singular perturbation problems

Aram L Karakhanyan

doi:10.1112/plms.12402

Regularity for the two phase singular perturbation problems

Aram L Karakhanyan

School of Mathematics

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

Abstract

We prove that an a priori bounded mean oscillation (BMO) gradient estimate for the two-phase singular perturbation problem implies Lipschitz regularity for the limits. This problem arises in the mathematical theory of combustion, where the reaction diffusion is modeled by the p -Laplacian. A key tool in our approach is the weak energy identity. Our method provides a natural and intrinsic characterization of the free boundary points and can be applied to more general classes of solutions.

Original language	English
Pages (from-to)	433-459
Journal	Proceedings of the London Mathematical Society
Volume	123
Issue number	5
Early online date	6 Apr 2021
DOIs	https://doi.org/10.1112/plms.12402
Publication status	Published - 30 Nov 2021

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https://arxiv.org/abs/1910.06997

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title = "Regularity for the two phase singular perturbation problems",

abstract = "We prove that an a priori bounded mean oscillation (BMO) gradient estimate for the two-phase singular perturbation problem implies Lipschitz regularity for the limits. This problem arises in the mathematical theory of combustion, where the reaction diffusion is modeled by the p -Laplacian. A key tool in our approach is the weak energy identity. Our method provides a natural and intrinsic characterization of the free boundary points and can be applied to more general classes of solutions.",

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AB - We prove that an a priori bounded mean oscillation (BMO) gradient estimate for the two-phase singular perturbation problem implies Lipschitz regularity for the limits. This problem arises in the mathematical theory of combustion, where the reaction diffusion is modeled by the p -Laplacian. A key tool in our approach is the weak energy identity. Our method provides a natural and intrinsic characterization of the free boundary points and can be applied to more general classes of solutions.

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DO - 10.1112/plms.12402

M3 - Article

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JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

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Regularity for the two phase singular perturbation problems

Abstract

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