Regularity for the two phase singular perturbation problems

Aram Karakhanyan

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arXiv · 1910.06997

Regularity for the two phase singular perturbation problems

Aram Karakhanyan

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Abstract

We prove that an a priori 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 modelled by the $p$-Laplacian. A key tool in our approach is the weak energy identity. Our method proves a natural and intrinsic characterization of the free boundary points and can be applied to more general classes of solutions.

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Aram Karakhanyan. 2019-10-15. Regularity for the two phase singular perturbation problems. https://arxiv.org/abs/1910.06997

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