arXiv subjects

Shangying Feng

Publications and source records attributed to Shangying Feng.

2 recordsLinked to original sources

arXiv2024

A $(ϕ_n, ϕ)$-Poincaré inequality on John domain

Given a bounded domain $Ω\subset {\mathbb R}^{n}$ with $n\ge2$, let $ϕ$ is a Young function satisfying the doubling condition with the constant $K_ϕ<2^{n}$. If $Ω$ is a John domain, we show that $Ω$ supports a $(ϕ_{n}, ϕ)$-Poincaré inequality. Conversely, assume additionally that $Ω$ is simply connected domain when $n=2$ or a bounded domain which is quasiconformally equivalent to some uniform domain when $n\ge3$. If $Ω$ supports a $(ϕ_n, ϕ)$-Poincaré inequality, we show that it is a John domain.

math.FA↗

arXiv2023

A $(ϕ_\frac{n}{s}, ϕ)$-Poincaré inequality in John domain

Let $Ω$ be a bounded domain in $\mathbb{R}^n$ with $n\ge2$ and $s\in(0,1)$. Assume that $ϕ: [0, \infty) \to [0, \infty)$ be a Young function obeying the doubling condition with the constant $K_ϕ<2^{\frac{n}{s}}$. We demonstrate that $Ω$ supports a $(ϕ_\frac{n}{s}, ϕ)$-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 $n\ge3$ or a simply connected domain when $n=2$. We demonstrate $Ω$ is a John domain if a $(ϕ_\frac{n}{s}, ϕ)$-Poincaré inequality holds.

math.FA↗