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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.
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.
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...
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。
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...
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...
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。
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...
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},...
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...
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 ...

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