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

By virtue of an operator-theoretical approach, we deal with hyperbolic singular perturbation problems for integrodifferential equations. New convergence theorems for such singular perturbation problems are obtained, which generalize some previous results by This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, an...

We investigate the asymptotic behavior of some anisotropic diffusion problems and give some estimates on the rate of convergence of the solution toward its limit. We also relate this type of elliptic problems to problems set in cylinder becoming unbounded in some directions and show how some information on one type leads to information for the other type and conversely. 1. A model problem The g...