11 papers
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.
Constructing Discontinuous but Locally Bounded Rational Functions using Łojasiewicz Inequalities
Adam Coffman, Yifei Pan
For real multivariate polynomials and both vanishing at a point, if the zero set of is contained in the zero set of , then there exists a rational function of the fo…
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…
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…
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…