1 citations · 2 across the 16 of their papers we have counts for
17 papers
A Hopf Lemma for Holomorphic Maps into Hyperquadrics
Xiaojun Huang, Yuan Zhang, Weixia Zhu
More than twenty years ago, Baouendi and the first author proved that a holomorphic map between hyperquadrics of the same signature is either totally degenerate or has a nonvanishi…
Unique continuation for at infinity
Yifei Pan, Yuan Zhang
Motivated by Landis's conjecture on unique continuation at infinity for the Laplacian, we study the corresponding property for the Cauchy-Riemann operator. We prove that every weak…
Constructing bounded pseudoconvex domains of finite D'Angelo type with prescribed weak loci
Martino Fassina, Yifei Pan, Yuan Zhang
We construct smoothly bounded pseudoconvex or convex domains in whose weakly pseudoconvex loci realize prescribed closed sets.
On a Local Radial Rigidity Phenomenon of Elliptic Systems on Riemannian Manifolds
Yifei Pan, Yu Yan, Yuan Zhang
In this paper, we study local radial rigidity phenomena for a broad class of general-order elliptic systems on Riemannian manifolds via a reduction to singular ordinary differentia…
Non-quadratic solutions to the Monge-Ampère equation
Yifei Pan, Yuan Zhang
We construct ample smooth strictly plurisubharmonic non-quadratic solutions to the Monge-Ampère equation on either cylindrical type domains or the whole complex Euclidean space $\m…
On homotopy formulae for product domains: Nijenhuis-Woolf's formulae and optimal Sobolev estimates
Liding Yao, Yuan Zhang
We construct homotopy formulae for forms on the product domain , where each…
Unique continuation of Schrödinger-type equations for II
Yifei Pan, Yuan Zhang
In this paper, we extend our earlier unique continuation results \cite{PZ2} for the Schrödinger-type inequality on a domain in by removin…
Continuous Sobolev functions with singularity on arbitrary real-analytic sets
Yifei Pan, Yuan Zhang
Near every point of a real-analytic set in , we make use of Hironaka's resolution of singularity theorem to construct a family of continuous functions in $W^{1, 1}_{lo…
Unique continuation of Schrödinger-type equations for
Yifei Pan, Yuan Zhang
The purpose of this paper is to study the unique continuation property for a Schrödinger-type equation on a domain in , where the solution m…
Unique continuation for a gradient inequality with potential
Adam Coffman, Yifei Pan, Yuan Zhang
We establish a unique continuation property for solutions of the differential inequality , where is locally integrable on a domain in .…
On solutions to near infinity
Yifei Pan, Yuan Zhang
We investigate the unique continuation property and the sign changing behavior of weak solutions to near infinity under certain conditions on the blow-up rate of the pote…
Sobolev regularity of the canonical solutions to on product domains
Yuan Zhang
Let be a product domain in , where each slice has smooth boundary. We observe that the canonical solution operator for the equation on i…
Optimal Sobolev regularity of on the Hartogs triangle
Yifei Pan, Yuan Zhang
In this paper, we show that for each , there exists a solution operator to the problem on the Hartogs triangle that maintains t…
Weighted Sobolev estimates of the truncated Beurling operator
Yifei Pan, Yuan Zhang
Given a bounded planar domain with boundary, , and a weight , we show that the corresponding truncated Beurling trans…
Optimal regularity for on the Hartogs triangle
Yuan Zhang
In this paper, we prove weighted estimates for the canonical solutions on product domains. As an application, we show that if , the equation…
Unique continuation for with square-integrable potentials
Yifei Pan, Yuan Zhang
In this paper, we investigate the unique continuation property for the inequality , where is a vector-valued function from a domain in …
Hölder estimates for the problem for forms on product domains
Yifei Pan, Yuan Zhang
The purpose of this paper is to study Hölder estimates for the problem for forms on products of general planar domains. As indicated by an example of Stein a…