Perturbation of elliptic operators in 1-sided NTA domains satisfying the capacity density condition

2019/01/24 by Murat Akman, Steve Hofmann, Akman, Murat +5
Computer Science · Mathematics · Social Sciences · #31B05 #35J08 #35J25 #42B25 #42B37 #42B99 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Military, Security, and Education Studies

paper · pdf · doi:10.48550/arxiv.1901.08261

openalex publication_date 2019/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Ω⊂ℝⁿ⁺¹, n≥ 2, be a 1-sided non-tangentially accessible domain (aka uniform domain), i.e., a set which satisfies the interior Corkscrew and Harnack chain conditions, respectively scale-invariant/quantitative versions of openness and path-connectedness. Assume that Ω satisfies the so-called capacity density condition. Let L₀u=-div(A₀∇ u), Lu=-div(A∇ u) be two real (non-necessarily symmetric) uniformly elliptic operators, and write ω_L0, ω_L for the associated elliptic measures. The goal of this program is to find sufficient conditions guaranteeing that ω_L satisfies an A_∞-condition or a RH_q-condition with respect to ω_L0. We show that if the discrepancy of the two matrices satisfies a natural Carleson measure condition with respect to ω_L0, then ω_L∈ A_∞(ω_L0). Moreover, ω_L∈ RH_q(ω_L0) for any given 1

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