Uniform Lipschitz estimates up to the boundary for singular perturbation problem for some nonlinear elliptic PDEs with unbounded ingredients

J Ederson M Braga,J Gleison Carneiro,Diego R Moreira

doi:10.1016/j.na.2023.113283

Uniform Lipschitz estimates up to the boundary for singular perturbation problem for some nonlinear elliptic PDEs with unbounded ingredients

J Ederson M Braga, J Gleison Carneiro + Show 1 more

https://doi.org/10.1016/j.na.2023.113283

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Journal: Nonlinear Analysis

Publication Date: Mar 31, 2023

Affiliation: Universidade Federal do Ceará

#Uniform Lipschitz Estimates #Singular Perturbation Problem + Show 8 more

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Abstract

We prove uniform up to the boundary gradient estimates for one phase nonlinear inhomogeneous singular perturbation problems with unbounded measurable ingredients governed by fully nonlinear elliptic equations. We present similar results for quasilinear PDEs with bounded RHS. Our proof is based on the Lipschitz regularity up to the boundary for free boundary problems (FBP) found in Braga and Moreira (2022).

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