Dachun Yang

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20242026

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4 papers · 1 filter

math.AP2025

Robin Problems of Elliptic Equations on Rough Domains: Hölder Regularity, Green's Functions, and Harmonic Measures

Jiayi Wang, Dachun Yang, Sibei Yang

Let $n \geq 2$ and $s \in (n - 2, n)$ . Assume that $Ω \subset R^{n}$ is a one-sided bounded non-tangentially accessible domain with $s$ -Ahlfors regular boundary and $σ$ is the surf…

math.FA2025

Fractional Heat Semigroup Characterization of Distances from Functions in Lipschitz Spaces to Their Subspaces

Feng Dai, Eero Saksman, Dachun Yang +2

Let $Λ_{s}$ denote the inhomogeneous Lipschitz space of order $s \in (0, \infty)$ on $R^{n}$ . This article characterizes the distance $d(f, V)_{Λ_s}: = \inf_{g\in V} \|f-g\|_{Λ_s…

math.AP2025

Equivalent Characterizations and Applications of Fractional Sobolev Spaces with Partially Vanishing Traces on $(ε, δ, D)$ -Domains Supporting $D$ -Adapted Fractional Hardy Inequalities

Jun Cao, Dachun Yang, Qishun Zhang

Let $Ω \subset R^{n}$ be an $(ε, δ, D)$ -domain, with $ε \in (0, 1]$ , $δ \in (0, \infty]$ , and $D \subset \partial Ω$ being a closed part of $\partial Ω$ , which is a general open connec…

math.AP2025

Equivalent Characterizations and Their Applications of Solvability of $L^{p}$ Poisson--Robin(-Regularity) Problems on Rough Domains

Xuelian Fu, Dachun Yang, Sibei Yang

Let $n \geq 2$ , $Ω \subset R^{n}$ be a bounded one-sided chord arc domain, and $p \in (1, \infty)$ . In this article, we study the (weak) $L^{p}$ Poisson--Robin(-regularity) problem fo…

Robin Problems of Elliptic Equations on Rough Domains: Hölder Regularity, Green's Functions, and Harmonic Measures

Fractional Heat Semigroup Characterization of Distances from Functions in Lipschitz Spaces to Their Subspaces

Equivalent Characterizations and Applications of Fractional Sobolev Spaces with Partially Vanishing Traces on (ε,δ,D)-Domains Supporting D-Adapted Fractional Hardy Inequalities

Equivalent Characterizations and Their Applications of Solvability of Lp Poisson--Robin(-Regularity) Problems on Rough Domains

Equivalent Characterizations and Applications of Fractional Sobolev Spaces with Partially Vanishing Traces on $(ε, δ, D)$ -Domains Supporting $D$ -Adapted Fractional Hardy Inequalities

Equivalent Characterizations and Their Applications of Solvability of $L^{p}$ Poisson--Robin(-Regularity) Problems on Rough Domains