Perturbations of elliptic operators in chord arc domains

2012/10/20 by Emmanouil Milakis, Jill Pipher, Milakis, Emmanouil +3
Mathematics · #(31B05) #35J25 #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Holomorphic and Operator Theory #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1210.5591

openalex publication_date 2012/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the boundary regularity of solutions to divergence form operators which are small perturbations of operators for which the boundary regularity of solutions is known. An operator is a small perturbation of another operator if the deviation function of the coefficients satisfies a Carleson measure condition with small norm. We extend Escauriaza's result on Lipschitz domains to chord arc domains with small constant. In particular we prove that if L₁ is a small perturbation of L₀ and log k₀ has small BMO norm so does log k₁. Here k_i denotes the density of the elliptic measure of L_i with respect to the surface measure of the boundary of the domain.

Related

• Divergence form operators in Reifenberg flat domains
• Carleson perturbations of locally Lipschitz elliptic operators
• Harmonic Analysis on chord arc domains
• Generalized Carleson perturbations of elliptic operators and\n applications
• Perturbation Theory for Second Order Elliptic Operators with BMO Antisymmetric Part