Related papers: A Korn-type inequality in SBD for functions with s…
We study the Riemannian distance function from a fixed point (a point-wise target) of Euclidean space in the presence of a compact obstacle bounded by a smooth hypersurface. First, we show that such a function is locally semiconcave with a…
The goal of this work is to show that the generalized Korn inequality that replaces the symmetric part of the differential matrix in the classical Korn inequality by its trace-free part is valid over John domains and weighted Sobolev…
The aim of the paper is to show that the solutions to variational problems with non-standard growth conditions satisfy a corresponding variational inequality without any smallness assumptions on the gap between growth and coercitivity…
We consider the model describing the vertical motion of a ball falling with constant acceleration on a wall and elastically reflected. The wall is supposed to move in the vertical direction according to a given periodic function $f$. We…
In this paper, we address the random sampling problem for the class of Mellin band-limited functions BT which is concentrated on a bounded cube. It is established that any function in BT can be approximated by an element in a…
We propose a geometric method for quantifying the difference between parametrized curves in Euclidean space by introducing a distance function on the space of parametrized curves up to rigid transformations (rotations and translations).…
We prove that convex functions of finite order on the real line and subharmonic functions of finite order on finite dimensional real space, bounded from above outside of some set of zero relative Lebesgue density, are bounded from above…
Shape estimation and object reconstruction are common problems in image analysis. Mathematically, viewing objects in the image plane as random sets reduces the problem of shape estimation to inference about sets. Currently existing…
We condition a Brownian motion on having an atypically small $L_2$-norm on a long time interval. The obtained limiting process is a non-stationary Ornstein-Uhlenbeck process.
Strain correlation functions in two-dimensional isotropic elastic bodies are shown both theoretically (using the general structure of isotropic tensor fields) and numerically (using a glass-forming model system) to depend on the coordinates…
We prove that the Hausdorff dimension of the set of points where a function in the Zygmund class in the euclidean space has bounded divided differences, is bigger or equal to 1. A similar result for functions in the Small Zygmund class is…
A smooth rigidity inequalitiy provides an explicit lower bound for the $(d+1)$-st derivatives of a smooth function $f$, which holds, if $f$ exhibits certain patterns, forbidden for polynomials of degree $d$. The main goal of the present…
We prove that the optimal error of recovery in the $L_2$ norm of functions from a class $\bF$ can be bounded above by the value of the Kolmogorov width of $\bF$ in the uniform norm. We demonstrate on a number of examples of $\bF$ from…
This paper studies the second moment boundedness of solutions of linear stochastic delay differential equations. First, we give a framework, for general $\mathrm{N}$-dimensional linear stochastic differential equations with a single…
In this paper, we introduce a symmetrization technique for the distributional gradient of a function of bounded variation in the anisotropic setting. This generalizes the result obtained in the Euclidean case in…
We study the existence of $L^2$ normalized solutions for nonlinear Schr\"odinger equations and systems. Under new Palais-Smale type conditions we develop new deformation arguments for the constraint functional on $S_m=\{ u; \,…
We introduce a process, that we call "shearing", which for any given normal Loewner chain produces a normal Loewner chain made of shears automorphisms. As an application, and in stringent contrast to the one-dimensional case, we prove the…
We consider stochastic differential systems driven by a Brownian motion and a Poisson point measure where the intensity measure of jumps depends on the solution. This behavior is natural for several physical models (such as Boltzmann…
In this paper we prove an integral representation formula for a general class of energies defined on the space of generalized special functions of bounded deformation ($GSBD^p$) in arbitrary space dimensions. Functionals of this type…
The purpose of the present paper is to establish explicit bounds on moderate deviation probabilities for a rather general class of geometric functionals enjoying the stabilization property, under Poisson input and the assumption of a…