Uniform regularity for degenerate elliptic equations in perforated domains

2023/11/17 by Zhongwei Shen, Shen, Zhongwei, Jinping Zhuge +1
Computer Science · Engineering · Mathematics · #35B27 #35J70 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2311.10258

openalex publication_date 2023/11/17 · openalex created_date 2023/11/21 · openalex updated_date 2026/07/28

Abstract

This paper is concerned with a class of degenerate elliptic equations with rapidly oscillating coefficients in periodically perforated domains, which arises in the study of spectrum problems for uniformly elliptic equations in perforated domains. We establish a quantitative convergence rate and obtain the uniform weighted Lipschitz and W^1,p estimates.

Related

• Homogenization of Boundary Value Problems in Perforated Lipschitz Domains
• Uniform W^{1, p} Estimates and Large-Scale Regularity for Dirichlet Problems in Perforated Domains
• Uniform Regularity Estimates in Homogenization Theory of Elliptic System with Lower Order terms
• Uniformly Degenerate Elliptic Equations with Varying Characteristic Exponents
• Homogenization of Elliptic Systems with Neumann Boundary Conditions