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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Heintze Karcher type inequalities on capillary hypersurfaces in hyperbolic space
双曲空间 毛细管超表面 海因茨·卡彻型不等式
2023/4/23
In this talk, I will introduce our recent result on Heintze Karcher type inequalities for capillary hypersurfaces supported on different types of umbilical hypersurfaces in hyperbolic space. I will in...
Quasilinear elliptic equations and weighted Sobolev-Poincare inequalities with distributional weights
Quasilinear equations weighted integral inequalities elliptic regularity
2012/4/16
We introduce a class of weak solutions to the quasilinear equation $-\Delta_p u = \sigma |u|^{p-2}u$ in an open set $\Omega\subset\mathbf{R}^n$. Here $p>1$, and $\Delta_p u$ is the $p$-Laplacian opera...
On critical cases of Sobolev's inequalities for Heisenberg groups
Heisenberg group Sobolev's inequality Brezis-Gallouet-Wainger inequality
2011/10/17
This paper deal with the problem of Sobolev imbedding in the critical cases. We prove some Trudinger-type inequalities on the whole Heisenberg group, extending to this context the Euclidean results by...
On critical cases of Sobolev's inequalities for Carnot groups
Carnot group Sobolev's inequality Brezis-Gallouet-Wainger inequality
2011/10/15
In this paper we deal with the problem of Sobolev imbedding in thecritical cases on Carnot groups. We prove some Trudinger-type inequalities on the whole Carnot group, extending to this context the Eu...
Weighted Isoperimetric Inequalities and Applications to Elliptic Equations
Relative isoperimetric inequality weighted perimeter degenerate elliptic equations
2011/9/21
Abstract: In this paper we study some weighted isoperimetric inequalities relative to cones of $\mathbb{R}^{N}$. We give some information on the structure of those measures admitting as isoperimetric ...
Isolated Singularities of Nonlinear Polyharmonic Inequalities
Isolated singularity Polyharmonic Analysis of PDEs
2011/9/19
Abstract: We obtain results for the following question where $m\ge 1$ and $n\ge 2$ are integers. {\bf Question.} For which continuous functions $f\colon [0,\infty)\to [0,\infty)$ does there exist a co...
An Interior Gradient Estimate for a class of Second Order Partial Differential Inequalities
Interior Gradient Estimate class of Second Order Partial Differential Inequalities
2011/2/22
In this paper, we show a uniform gradient estimate for functions u defined on a domain
in Euclidian space RN which satisfy a system of N second order partial differential inequalities of the followi...
Isoperimetric and Sobolev inequalities on hypersurfaces in sub-Riemannian Carnot groups
Carnot groups Sub-Riemannian Geometry Hypersurfaces Isoperimetric Inequality
2011/1/20
In this paper we shall study smooth submanifolds immersed in a k-step Carnot group G of homogeneous dimension Q. Our main result is an isoperimetric inequality for the case of a C2-smooth compact hype...
On comparison theorems for elliptic inequalities
Nonlinear elliptic operators Unbounded domains
2010/11/29
Suppose that is a non-empty open subset of Rn, n ≥ 2. Let us denote: R0,R1 = {x ∈ : R0 < |x| < R1} and R0,R1 = {x ∈ @ : R0 < |x| < R1}. By Bx r we mean the open ball in Rn of radius r > 0 a...
Differential Harnack inequalities for nonlinear heat equations with potentials under the Ricci flow
Differential Harnack inequality Interpolated Harnack inequality Nonlinear
2010/12/1
In this paper, we prove several differential Harnack inequalities for positive solutions of nonlinear (backward) heat equations with different potentials under the Ricci flow. In particular, for a clo...
Gaussians Rarely Extremize Adjoint Fourier Restriction Inequalities For Paraboloids
Gaussians Rarely Extremize Adjoint Fourier Restriction Inequalities Paraboloids
2011/1/19
Let Pd−1 be the paraboloid in Rd,Pd−1 = {(y′, yd) ∈ Rd−1 × R : yd = |y′|2/2}.Equip Pd−1 with the appropriately dilation-invariant measure on Rd defined by Z Rd f(y′, yd) d(y...
ERRATA: Coefficient inequalities for certain classes of Ruscheweyh type analytic functions
Errata Convolution Ruscheweyh derivative Uniformly starlike and Uniformly convex
2010/1/25
The purpose of this note is to give some corrections for our published article in [1].