26 citations · 68 across the 21 of their papers we have counts for
22 papers
Global solutions to the fully nonlinear obstacle problem
Yi Cao, Dongsheng Li
In this paper, we investigate global solutions to the fully nonlinear obstacle problem. We prove that, after factoring out invariant directions, the coincidence set of any global s…
Interior pointwise estimates for Stokes systems in divergence form
Rong Dong, Dongsheng Li
Interior pointwise estimates are established for Stokes systems in divergence form where no continuity in time variable is assumed for the coefficients and the given data…
quasiconformal mappings and a Bernstein type theorem over exterior domains in
Dongsheng Li, Rulin Liu
We establish the Hölder estimate and the asymptotic behavior at infinity for -quasiconformal mappings over exterior domains in . As a consequence, we prove an exte…
Interior regularity for Stokes systems
Rong Dong, Dongsheng Li, Lihe Wang
A new iteration method is represented to study the interior regularity for Stokes systems both in divergence form and in non-divergence form. By the iteration, we improve t…
Estimates for Elliptic Equations on Domains
Dongsheng Li, Xuemei Li, Kai Zhang
In this paper, a new method is represented to investigate boundary estimates for elliptic equations, which is, roughly speaking, to derive boundary estimates fr…
Estimates for Solution Sets of Fully Nonlinear Elliptic inequalities on Domains
Dongsheng Li, Xuemei Li
In this paper, we establish boundary estimates for on domains with as and boundary values. Instead of straight…
An Extension of Caldern-Zygmund type singular integral
Quansen Jiu, Dongsheng Li, Huan Yu
In this paper, we consider a kind of singular integral which can be viewed as an extension of the classical Caldern-Zygmund type singular integral. We establish an e…
Regularity for fully nonlinear elliptic equations with oblique boundary conditions
Dongsheng Li, Kai Zhang
In this paper, we obtain a series of regularity results for viscosity solutions of fully nonlinear elliptic equations with oblique derivative boundary conditions. In particular, we…
A note on the Harnack inequality for elliptic equations in divergence form
Dongsheng Li, Kai Zhang
In 1957, De Giorgi [3] proved the Hölder continuity for elliptic equations in divergence form and Moser [7] gave a new proof in 1960. Next year, Moser [8] obtained the Harnack ineq…
Pointwise Boundary Differentiability of Solutions of Elliptic Equations
Yongpan Huang, Dongsheng Li, Kai Zhang
In this paper, we give pointwise geometric conditions on the boundary which guarantee the differentiability of the solution at the boundary. Precisely, the geometric conditions are…
interior estimates of fully nonlinear elliptic equations
Dongsheng Li, Kai Zhang
In this paper, we generalize the interior estimates of fully nonlinear elliptic equations that were obtained by Caffarelli in [1]. The generalizations are carried out in…
An Optimal Geometric Condition on Domains for Boundary Differentiability of Solutions of Elliptic Equations
Dongsheng Li, Kai Zhang
In this paper, a geometric condition on domains will be given which guarantees the boundary differentiability of solutions of elliptic equations, that is, the solutions are differe…
Existence and boundary asymptotic behavior of large solutions of Hessian equations
Shanshan Ma, Dongsheng Li
In this paper, we establish the existence of large solutions of Hessian equations and obtain a new boundary asymptotic behavior of solutions.
Asymptotic behavior at infinity of solutions of Monge-Ampère equations in half spaces
Xiaobiao Jia, Dongsheng Li, Zhisu Li
We prove that any convex viscosity solution of outside a bounded domain of tends to a quadratic polynomial at infinity with rate at least $\frac{x_n…
Boundary Hölder Regularity for Elliptic Equations
Yuanyuan Lian, Kai Zhang, Dongsheng Li +1
This paper investigates the relation between the boundary geometric properties and the boundary regularity of the solutions of elliptic equations. We prove by a new unified method…
Symmetry and Approximate Symmetry of a Nonlinear Elliptic Problem over a Ring
Alaa Haj Ali, Dongsheng Li, Peiyong Wang
A singularly perturbed free boundary problem arising from a real problem associated with a Radiographic Integrated Test Stand concerns a solution of the equation in a d…
A pointwise approach to rigidity of almost graphical self-shrinking solutions of mean curvature flows
Dongsheng Li, Yingfeng Xu, Yu Yuan
We prove rigidity of any properly immersed noncompact Lagrangian shrinker with single valued Lagrangian angle for Lagrangian mean curvature flows. Our pointwise approach also provi…
A Bernstein problem for special Lagrangian equations in exterior domains
Dongsheng Li, Zhisu Li, Yu Yuan
We establish quadratic asymptotics for solutions to special Lagrangian equations with supercritical phases in exterior domains. The method is based on an exterior Liouville type re…
On the exterior Dirichlet problem for Hessian quotient equations
Dongsheng Li, Zhisu Li
In this paper, we establish the existence and uniqueness theorem for solutions of the exterior Dirichlet problem for Hessian quotient equations with prescribed asymptotic behavior…
Global estimates for singular fully nonlinear elliptic equations with right hand side terms
Dongsheng Li, Zhisu Li
We establish in this paper \emph{a priori} global estimates for singular fully nonlinear elliptic equations with right hand side terms. The method is to slide parab…
Global estimates for a type of singular fully nonlinear elliptic equations
Dongsheng Li, Zhisu Li
We obtain global estimates for a type of singular fully nonlinear elliptic equations where the right hand side term belongs to . The main idea of the proof is t…
Existence of Smooth Solutions of the Navier-Stokes Equations
Dongsheng Li
In this paper, we prove existence of smooth solutions of the Navier-Stokes equations that gives a positive answer to the problem proposed by Fefferman [3].