10 citations · 25 across the 15 of their papers we have counts for
15 papers
On one-space dimensional parabolic equations with measurable coefficients: Sobolev estimates and the Alexandrov maximum principle
Hongjie Dong, Zongyuan Li
Let and set and . We construct a coefficient , smooth outside a compact set of Lebesgue measure zero, for which the $W^{1,2}_{…
Asymptotic expansions for harmonic functions at conical boundary points
Dennis Kriventsov, Zongyuan Li
We prove three theorems about the asymptotic behavior of solutions to the homogeneous Dirichlet problem for the Laplace equation at boundary points with tangent cones. First, u…
Asymptotics of harmonic functions in the absence of monotonicity formulas
Zongyuan Li
In this article, we study the asymptotics of harmonic functions. A typical method is by proving monotonicity formulas of a version of rescaled Dirichlet energy, and use it to study…
Unique continuation for Robin problems with non-smooth potentials
Zongyuan Li
In this work, we study the unique continuation properties of Robin boundary value problems with Robin potentials . Our results generalize earlier ones in…
On the uniqueness of variable coefficient Schrödinger equations
Serena Federico, Zongyuan Li, Xueying Yu
We prove unique continuation properties for linear variable coefficient Schrödinger equations with bounded real potentials. Under certain smallness conditions on the leading coeffi…
Mixed boundary value problems for parabolic equations in Sobolev spaces with mixed-norms
Jongkeun Choi, Hongjie Dong, Zongyuan Li
We establish -estimates and solvability for mixed Dirichlet-conormal problems for parabolic equations in a cylindrical Reifenberg-flat domain with a rough time-dependent s…
The Dirichlet-conormal problem for the heat equation with inhomogeneous boundary conditions
Hongjie Dong, Zongyuan Li
We consider the mixed Dirichlet-conormal problem for the heat equation on cylindrical domains with a bounded and Lipschitz base and a time-dependent separat…
Quantitative unique continuation for Robin boundary value problems on domains
Zongyuan Li, Weinan Wang
In this paper, we prove two unique continuation results for second order elliptic equations with Robin boundary conditions on domains. The first one is a sharp vanishing…
Optimal regularity of mixed Dirichlet-conormal boundary value problems for parabolic operators
Jongkeun Choi, Hongjie Dong, Zongyuan Li
We obtain the regularity of solutions in Sobolev spaces for the mixed Dirichlet-conormal problem for parabolic operators in cylindrical domains with time-dependent separations, whi…
The conormal and Robin boundary value problems in nonsmooth domains satisfying a measure condition
Hongjie Dong, Zongyuan Li
We consider elliptic equations and systems in divergence form with the conormal or the Robin boundary conditions, with small BMO (bounded mean oscillation) or variably partially sm…
The Dirichlet-conormal problem with homogeneous and inhomogeneous boundary conditions
Hongjie Dong, Zongyuan Li
We consider the mixed Dirichlet-conormal problem on irregular domains in . Two types of regularity results will be discussed: the regularity and a non-tange…
Norm inflation for the Boussinesq system
Zongyuan Li, Weinan Wang
We prove the norm inflation phenomena for the Boussinesq system on . For arbitrarily small initial data in the negative-order Besov spaces $\dot{B}^{-1}_{\…
estimate for oblique derivative problem with mean Dini coefficients
Hongjie Dong, Zongyuan Li
We consider second-order elliptic equations in non-divergence form with oblique derivative boundary conditions. We show that any strong solutions to such problems are twice continu…
Optimal regularity for a Dirichlet-conormal problem in Reifenberg flat domain
Jongkeun Choi, Hongjie Dong, Zongyuan Li
We study the divergence form second-order elliptic equations with mixed Dirichlet-conormal boundary conditions. The unique solvability is obtained with being in the o…
On the Estimate for Oblique Derivative Problem in Lipschitz Domains
Hongjie Dong, Zongyuan Li
The aim of this paper is to establish estimate for non-divergence form second-order elliptic equations with the oblique derivative boundary condition in domains with small…