Derivative estimates of solutions of elliptic systems in narrow regions
We establish derivative estimates of solution of elliptic system in narrow regions.
math.AP↗
arXiv subjects
Haigang Li
Publications and source records attributed to Haigang Li.
Monge-Ampere equation on exterior domains
We consider the Monge-Ampère equation $\det(D^2u)=f$ where $f$ is a positive function in $\mathbb R^n$ and $f=1+O(|x|^{-β})$ for some $β>2$ at infinity. If the equation is globally defined on $\mathbb R^n$ we classify the asymptotic behavior of solutions at infinity. If the equation is defined outside a convex bounded set we solve the corresponding exterior Dirichlet problem. Finally we prove for $n\ge 3$ the existence of global solutions with prescribed asymptotic behavior at infinity. The assumption $β>2$ is sharp for all the results in this article.
math.AP↗
Gradient Estimates for Parabolic Systems from Composite Material
In this paper we derive $W^{1,\infty}$ and piecewise $C^{1,α}$ estimates for solutions, and their $t-$derivatives, of divergence form parabolic systems with coefficients piecewise Hölder continuous in space variables $x$ and smooth in $t$. This is an extension to parabolic systems of results of Li and Nirenberg on elliptic systems. These estimates depend on the shape and the size of the surfaces of discontinuity of the coefficients, but are independent of the distance between these surfaces.
math.AP↗
On the exterior Dirichlet problem for Hessian equations
In this paper, we establish a theorem on the existence of the solutions of the exterior Dirichlet problem for Hessian equations with prescribed asymptotic behavior at infinity. This extends a result of Caffarelli and Li for the Monge-Ampère equation to Hessian equations.
math.AP↗
Harmonic maps on domains with piecewise Lipschitz continuous metrics
For a bounded domain equipped with a piecewise Lipschitz continuous Riemannian metric g, we consider harmonic map from $(Ω, g)$ to a compact Riemannian manifold $(N,h)\subset\mathbb R^k$ without boundary. We generalize the notion of stationary harmonic map and prove the partial regularity. We also discuss the global Lipschitz and piecewise $C^{1,α}$-regularity of harmonic maps from $(Ω, g)$ manifolds that support convex distance functions.
math.AP↗