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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars："Sobolev extensions"(7)&(8)
Sobolev扩展 Whitney扩展 技术变体
2023/11/29
I will give an introduction to Sobolev extensions, including the use of variants of the Whitney extension technique. I will concentrate on the basics of the theory.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars："Sobolev extensions"(5)&(6)
Sobolev扩展 Whitney扩展 技术变体
2023/11/29
I will give an introduction to Sobolev extensions, including the use of variants of the Whitney extension technique. I will concentrate on the basics of the theory.
Sobolev不等式关于梯度的最优稳定性
Sobolev不等式 梯度 最优稳定性
2023/1/5
We prove a sharp quantitative version of the p-Sobolev inequality for any 1ol on the strongest possible distance from the class of optimal functions. Surprisingly, the sharp exponent...
Sobolev不等式关于梯度的最优稳定性（张翼）
Sobolev不等式 梯度 最优稳定性
2023/2/22
We prove a sharp quantitative version of the p-Sobolev inequality for any 1ol on the strongest possible distance from the class of optimal functions. Surprisingly, the sharp exponent...
研究一类带Hardy-Sobolev临界指数的Kirchhoff型方程其中Ω⊂R3是一个有界开区域且边界∂Ω光滑，0∈Ω，a，b≥0且a+b>0，λ>0，0 < q < 1，0≤s<1。利用变分方法，获得该问题正解的存在性结果。
Growth of Sobolev norms in the cubic defocusing nonlinear Schrodinger equation
Sobolev norms cubic defocusing nonlinear Schrodinger equation
2015/9/25
We consider the cubic defocusing nonlinear Schr¨odinger equation in the two dimensional torus. Fix s > 1. Colliander, Keel, Staffilani, Tao and Takaoka proved in [CKS+10] the existence of solutions wi...
Let M be a cg-connected manifold. Let L be a second-order
differential operator with real cg(R) coefficients on M and such that L1 0 (i.e., L
has no zero-order term). Assume that there exists a posi...
LOGARITHMIC SOBOLEV INEQUALITIES FOR FINITE MARKOV CHAINS
Sobolev inequality MARKOV CHAINS
2015/8/26
This is an expository paper on the use of logarithmic Sobolev inequalities
for bounding rates of convergence of Markov chains on finite state
spaces to their stationary distributions. Logarithmic So...
We present a simple and direct proof of the equivalence of various
functional inequalities such as Sobolev or Nash inequalities. This
proof applies in the context of Riemannian or sub-elliptic geome...
Pseudo-Poincar¶e Inequalities and Applications to Sobolev Inequalities
Sobolev Inequalities Inequalities
2015/8/26
Most smoothing procedures are via averaging. Pseudo-Poincar¶e in-
equalities give a basic Lp-norm control of such smoothing procedures in terms
of the gradient of the function involved. When av...
LOGARITHMIC SOBOLEV INEQUALITIES FOR FINITE MARKOV CHAINS
Logarithmic sobolev limited markov chain the inequality
2015/7/14
LOGARITHMIC SOBOLEV INEQUALITIES FOR FINITE MARKOV CHAINS。
Ridgelets and the Representation of Mutilated Sobolev Functions
Sobolev spaces Fourier transform singularities ridgelets orthonormal ridgelets nonlinear approximation sparsity
2015/6/17
We show that ridgelets, a system introduced in [4], are optimal to represent smooth multivariate functions that may exhibit linear singularities. For instance, let {u · x − b > 0} be an arbitrar...
Absolute continuity of the best Sobolev constant of a bounded domain
Absolute continuity Lipschitz continuity p-Laplacian Rayleigh quotient Sobolev best constants
2012/6/7
Let $\lambda_{q}:=\inf{\Vert\nabla u\Vert_{L^{p}(\Omega)}^{p}/\Vertu\Vert_{L^{q}(\Omega)}^{p}:u\in W_{0}^{1,p}(\Omega)\setminus{0}} $, where $\Omega$ is a bounded and smooth domain of $\mathbb{R}^{N},...
New logarithmic Sobolev inequalities and an ε-regularity theorem for the Ricci flow
New logarithmic Sobolev inequalities ε-regularity theorem Ricci flow Differential Geometry
2012/5/24
In this note we prove a new \epsilon-regularity theorem for the Ricci flow. Let (M^n,g(t)) with t\in [-T,0] be a Ricci flow and H_{x} the conjugate heat kernel centered at a point (x,0) in the final t...
On Control Of Sobolev Norms For Some Semilinear Wave Equations With Localized Data
Control Sobolev Norms Some Semilinear Wave Equations Localized Data
2012/4/16
We establish new bounds of the Sobolev norms of solutions of semilinear wave equations for data lying in the Hs, s<1, closure of compactly supported data inside a ball of radius R, with R a fixed and ...