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In this talk, we first consider convex optimization whose smooth components have a locally Lipschitz continuous gradient and propose a first-order method for finding an epsilon-KKT solution. We then c...
In this note we show that reconstruction from magnitudes of frame coefficients (the so called “phase retrieval problem”) can be performed using Lipschitz continuous maps. Specifically we show that whe...
This paper gives geometric tools: comparison, Nash and Sobolev inequalities for pieces of the relevent Markov operators, that give useful bounds on rates of convergence for the Metropolis algorithm. A...
考察了完备的度量凸空间框架下满足具有变系数的Lipschitz条件的非自映射族并根据给定的边界条件和映射族构造了一个收敛序列{xn},然后证明了该序列的唯一极限正是映射族的唯一的公共不动点.最后给出了更广泛的结果.所得结果推广和改进了许多压缩型映射族的公共不动点定理.
Using the extrapolation of one-sided weights, we establish the boundedness of commutators generated by weighted Lipschitz functions and one-sided singular integral operators from weighted Lebesgue spa...
We define the isoperimetric constant for any locally finite metric space and we study the property of having isoperimetric constant equal to zero. This property, called Small Neighborhood property, cl...
在局部Lipschitz条件下,得到了任意给定时间区间上,正倒向重随机微分方程的解的存在唯一性结果.
研究单个连续障碍的反射倒向随机微分方程解的存在唯一性,其生成元关于y和z都是一致连续的,且不要求 有界,并在 的条件下给出反射倒向随机微分方程解的比较定理。运用逼近的思想处理反射项,用Lipschitz函数加无穷小项控制一致连续函数的方法处理z解,再结合Bihari不等式得到方程的唯一解。比较定理是通过Tanaka公式、Girsanov变换和Bihari不等式得到。
Abstract: Let $\Omega$ be a strongly Lipschitz domain of $\mathbb{R}^n$, whose complement in $\mathbb{R}^n$ is unbounded. Let $L$ be a second order divergence form elliptic operator on $L^2 (\Omega)$ ...
Abstract: We establish new Hoelder and Lipschitz estimates for viscosity solutions of a large class of elliptic and parabolic nonlinear integro-differential equations, by the classical Ishii-Lions's m...
Abstract: Let $\Omega$ be either $\mathbb{R}^n$ or an unbounded strongly Lipschitz domain of $\mathbb{R}^n$, and $\Phi$ be a continuous, strictly increasing, subadditive and positive function on $(0,\...
Abstract: The Lipschitz constant of a finite normal-form game is the maximal change in some player's payoff when a single opponent changes his strategy. We prove that games with small Lipschitz consta...
Abstract: We study the boundary integral operator induced from fractional Laplace equation in a bounded Lipschitz domain. As an application, we study the boundary value problem of a fractional Laplace...
Let us consider a Riemannian manifold M (either separable or non-separable). We prove that, for every " > 0, every Lipschitz function f : M ! R can be uniformly approximated by a Lipschitz, C1-smooth ...
The integrated density of states of a Schr¨odinger operator with random potential given by a homogeneous Gaussian field whose covariance function is continuous, compactly supported and has positive me...

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