Dachun Yang

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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.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…

math.AP2024

Global BMO-Sobolev Estimates for Second-Order Linear Elliptic Equations on Lipschitz Domains

Hongjie Dong, Dachun Yang, Sibei Yang

Let $n \geq 2$ and $Ω \subset R^{n}$ be a bounded Lipschitz domain. In this article, we establish first-order global regularity estimates in the scale of BMO spaces on $Ω$ for…

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

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

Global BMO-Sobolev Estimates for Second-Order Linear Elliptic Equations on Lipschitz 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