Regularity for the two phase singular perturbation problems

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Abstract / Description of output

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 languageEnglish
Pages (from-to)433-459
JournalProceedings of the London Mathematical Society
Issue number5
Early online date6 Apr 2021
Publication statusPublished - 30 Nov 2021


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