A degenerate fully nonlinear free transmission problem with variable exponents

2021/11/03 by Jesús David, Jesus, David
Computer Science · Mathematics · #35J70 #35R35 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Primary 35B65. Secondary 35J60

paper · pdf · doi:10.48550/arxiv.2111.02225

openalex publication_date 2021/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study degenerate fully nonlinear free transmission problems, where the degeneracy rate varies in the domain. We prove optimal pointwise regularity depending on the degeneracy rate. Our arguments consist of perturbation methods, relating our problem to a homogeneous, fully nonlinear, uniformly elliptic equation.

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