Regularity for the two phase singular perturbation problems
Analysis of PDEs
2021-04-20 v2
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 -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.
Cite
@article{arxiv.1910.06997,
title = {Regularity for the two phase singular perturbation problems},
author = {Aram Karakhanyan},
journal= {arXiv preprint arXiv:1910.06997},
year = {2021}
}