Related papers: A sharp Korn's inequality for piecewise $H^1$ spac…
In this paper we show that Korn's inequality \cite{ref:korn1906} holds for vector fields with a zero normal or tangential trace on a subset (of positive measure) of the boundary of Lipschitz domains. We further show that the validity of…
In this article, we propose a state of the art concerning the nodal and spectral minimal partitions. First we focus on the nodal partitions and give some examples of Courant sharp cases. Then we are interested in minimal spectral…
We give conditions on a knot on which the Morton-Franks-Williams inequality is not sharp. As applications, we show infinitely many examples of knots where the inequality is not sharp and also prove (by giving examples) that the deficit of…
In this paper we derive a necessary condition for finite element method (FEM) convergence in $H^1(\Omega)$ as well as generalize known sufficient conditions. We deal with the piecewise linear conforming FEM on triangular meshes for…
This paper can be seen as an attempt of rethinking the {\em Extra-Gradient Philosophy} for solving Variational Inequality Problems. We show that the properly defined {\em Reduced Gradients} can be used instead for finding approximate…
For a Lipschitz domain we show that solutions of certain first order systems are unique. This result is then applied to prove a crucial step for showing Korn's first inequality as well as to prove the 'infinitesimal rigid displacement lemma…
Motivated by indoor localization by tripwire lasers, we study the problem of cutting a polygon into small-size pieces, using the chords of the polygon. Several versions are considered, depending on the definition of the "size" of a piece.…
We show how to find a complete set of necessary and sufficient conditions that solve the fixed-parameter local congruence problem of immersions in $G$-spaces, whether homogeneous or not, provided that a certain $k^{\rm th}$ order jet bundle…
We prove a relative version of the fact that semiorthogonal decompositions of the bounded derived category of coherent sheaves are strongly constrained by the base locus of the canonical linear system. As an application we prove that the…
We establish the new main inequality as a minimizing criterion for minimal maps to products of $\mathbb{R}$-trees, and the infinitesimal new main inequality as a stability criterion for minimal maps to $\mathbb{R}^n$. Along the way, we…
We prove the sharp quantitative stability for a wide class of weighted isoperimetric inequalities. More precisely, we consider isoperimetric inequalities in convex cones with homogeneous weights. Inspired by the proof of such isoperimetric…
A proof for the lower bound is provided for the smallest eigenvalue of finite element equations with arbitrary conforming simplicial meshes. The bound has a similar form as the one by Graham and McLean [SIAM J. Numer. Anal., 44 (2006), pp.…
Inequalities are important features in the context of sequences of numbers and polynomials. The Bessenrodt--Ono inequality for partition numbers and Nekrasov--Okounkov polynomials has only recently been discovered. In this paper we study…
The current status concerning Hardy-type inequalities with sharp constants is presented and described in a unified convexity way. In particular, it is then natural to replace the Lebesgue measure $dx$ with the Haar measure $dx/x.$ There are…
It is often said that measuring a system's position must disturb the complementary property, momentum, by some minimum amount due to the Heisenberg uncertainty principle. Using a "weak-measurement", this disturbance can be reduced. One…
A homogeneous space G/H is said to have a compact Clifford-Klein form if there exists a discrete subgroup D of G that acts properly discontinuously on G/H, such that the quotient space D\G/H is compact. When n is even, we find every closed,…
In this paper we consider the variable inequality problem, that is, to find a solution of the inclusion given by the sum of a function and a point-to-cone application. This problem can be seen as a generalization of the classical system…
Motivated by some applications in signal processing and machine learning, we consider two convex optimization problems where, given a cone $K$, a norm $\|\cdot\|$ and a smooth convex function $f$, we want either 1) to minimize the norm over…
We study the sharp constant in the Morrey inequality for fractional Sobolev-Slobodecki\u{\i} spaces on the whole $\mathbb{R}^N$. By generalizing a recent work by Hynd and Seuffert, we prove existence of extremals, together with some…
We develop a stabilized cut finite element method for the convection problem on a surface based on continuous piecewise linear approximation and gradient jump stabilization terms. The discrete piecewise linear surface cuts through a…