Fully Nonlinear Singularly perturbed models with non-homogeneous degeneracy
Abstract
In our work we study non-variational, nonlinear singularly perturbed elliptic models enjoying a double degeneracy character with prescribed boundary value in a domain. In such a scenario, we establish the existence of solutions. We also prove that solutions are locally (uniformly) Lipschitz continuous, and they grow in a linear fashion. Moreover, solutions and their free boundaries possess a sort of measure-theoretic and weak geometric properties. Moreover, for a restricted class of non-linearities, we prove the finiteness of the (N-1)-dimensional Hausdorff measure of level sets. We also address a complete analysis concerning the asymptotic limit as the singular parameter, which is related to one-phase solutions of inhomogeneous nonlinear free boundary problems in flame propagation and combustion theory.
Keywords
Cite
@article{arxiv.2101.08664,
title = {Fully Nonlinear Singularly perturbed models with non-homogeneous degeneracy},
author = {João V. Silva and Elzon C. Júnior and Gleydson C. Ricarte},
journal= {arXiv preprint arXiv:2101.08664},
year = {2024}
}