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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Some recent progress on the gradient estimates for the insulated conductivity problem
绝缘 电导率 梯度估计 椭圆偏微分方程
2023/4/17
In this talk, I will describe an elliptic PDE that models electric conduction, and the electric field concentration phenomenon between closely spaced inclusions of high contrast. In the first part, I ...
Boundary Harnack principle and gradient estimates for fractional Laplacian perturbed by non-local operators
Harmonic function boundary Harnack principle gradient estimate
2016/1/20
Boundary Harnack principle and gradient estimates for fractional Laplacian perturbed by non-local operators.
The paper considers a manifold M evolving under the Ricci
ow and establishes a series of gradient
estimates for positive solutions of the heat equation on M. Among other results, we prove Li-Yau-ty...
Gradient estimates for porous medium and fast diffusion equations via FBSDE approach
Gradient estimates porous medium fast diffusion equations FBSDE approach Probability
2012/6/27
In this paper, we establish several gradient estimates for the positive solution of Porous Medium Equations (PMEs) and Fast Diffusion Equations (FDEs). Our proof is probabilistic and uses martingale t...
In this paper, we establish a Bochner type formula on Alexandrov spaces with Ricci curvature
bounded below. Yau’s gradient estimates for harmonic functions is also obtained on Alexandrov
spaces.
On gradient estimates for a nonlinear parabolic equation on Riemannian manifolds
Nonlinear parabolic equations Gradient estimates
2010/9/25
Let (M,g) be a complete noncompact Riemannian manifold. In this note, we derive a local gradient estimate for positive solution to a simple nonlinear parabolic equation
Coupling Property and Gradient Estimates of Lévy Processes via the Symbol
Coupling Property Gradient Estimates Lévy Processes via the Symbol
2010/11/11
We derive explicitly the coupling property for the transition semigroup of a L\'evy process and gradient estimates for the associated semigroup of transition operators. This is based on the asymptoti...
Gradient estimates for a simple nonlinear heat equation on manifolds
nonlinear heat equation gradient estimate
2010/11/29
In this paper, we study the gradient estimate for positive solutions to the following nonlinear heat equation problem ut − u = au log u + V u, u > 0 on the compact Riemannian manifold (M, g) of...