Lipschitz Continuity for Elliptic Free Boundary Problems with Dini Mean Oscillation Coefficients

2022/06/21 by Abdeslem Lyaghfouri, Lyaghfouri, Abdeslem
Computer Science · Mathematics · #35J15 #35R35 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2206.10239

openalex publication_date 2022/06/21 · openalex created_date 2022/06/24 · openalex updated_date 2026/07/28

Abstract

We establish local interior Lipschitz continuity of the solutions of a class of free boundary elliptic problems assuming the coefficients of the equation of Dini mean oscillation in at least one direction. The novelty in this regularity result lies in the fact that it allows discontinuous coefficients in all but one variable.

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