A (ϕ_(n)/(s), ϕ)-Poincaré inequality in John domain

2023/05/06 by Shangying Feng, Tian Liang, Feng, Shangying +1
Mathematics · #Analytic and geometric function theory #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.2305.04016

openalex publication_date 2023/05/06 · openalex created_date 2023/05/10 · openalex updated_date 2026/07/28

Abstract

Let Ω be a bounded domain in ℝⁿ with n≥2 and s∈(0,1). Assume that ϕ: [0, ∞) → [0, ∞) be a Young function obeying the doubling condition with the constant K_ϕ<2^(n)/(s). We demonstrate that Ω supports a (ϕ_(n)/(s), ϕ)-Poincaré inequality if it is is a John domain. Alternately, assume further that Ω is a bounded domain that is quasiconformally equivalent to some uniform domain when n≥3 or a simply connected domain when n=2. We demonstrate Ω is a John domain if a (ϕ_(n)/(s), ϕ)-Poincaré inequality holds.

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