Yuan Zhang

collaborators

4 papers

math.CV2022

Sobolev regularity of the canonical solutions to $\partial ˉ$ on product domains

Yuan Zhang

Let $Ω$ be a product domain in $C^{n}, n \geq 2$ , where each slice has smooth boundary. We observe that the canonical solution operator for the $\partial ˉ$ equation on $Ω$ i…

math.CV2022

Optimal Sobolev regularity of $\partial ˉ$ on the Hartogs triangle

Yifei Pan, Yuan Zhang

In this paper, we show that for each $k \in Z^{+}, p > 4$ , there exists a solution operator $T_{k}$ to the $\partial ˉ$ problem on the Hartogs triangle that maintains t…

math.CV2022

Unique continuation for $\partial ˉ$ with square-integrable potentials

Yifei Pan, Yuan Zhang

In this paper, we investigate the unique continuation property for the inequality $∣ \partial ˉ u ∣ \leq V ∣ u ∣$ , where $u$ is a vector-valued function from a domain in $C^{n}$ …

math.CV2020

Hölder estimates for the $\partial ˉ$ problem for $(p, q)$ forms on product domains

Yifei Pan, Yuan Zhang

The purpose of this paper is to study Hölder estimates for the $\partial ˉ$ problem for $(p, q)$ forms on products of general planar domains. As indicated by an example of Stein a…

Sobolev regularity of the canonical solutions to ∂ˉ on product domains

Optimal Sobolev regularity of ∂ˉ on the Hartogs triangle

Unique continuation for ∂ˉ with square-integrable potentials

Hölder estimates for the ∂ˉ problem for (p,q) forms on product domains

Sobolev regularity of the canonical solutions to $\partial ˉ$ on product domains

Optimal Sobolev regularity of $\partial ˉ$ on the Hartogs triangle

Unique continuation for $\partial ˉ$ with square-integrable potentials

Hölder estimates for the $\partial ˉ$ problem for $(p, q)$ forms on product domains