Related papers: Maximizers for the Stein-Tomas inequality
We present a unified study of first and second order necessary and sufficient optimality conditions for minimax and Chebyshev optimisation problems with cone constraints. First order optimality conditions for such problems can be formulated…
This note introduces a sufficient Linear Matrix Inequality (LMI) condition for the ultimate boundedness of a class of continuous-time dynamical systems with conic uncertain/nonlinear terms.
We derive optimal dimension independent constants in the classical Khintchine inequality between the $p$th and fourth moment for $p\ge 4$. As an application we deduce stability estimates for the Khintchine inequality between the $p$th and…
In this article we establish new improvements of the optimal Hardy inequality in the half space. We first add all possible linear combinations of Hardy type terms thus revealing the structure of this type of inequalities and obtaining best…
This paper deals with the optimization of Bolza problem with a system of convex and nonconvex, discrete and differential state variable inequality constraints of second order by deriving necessary and sufficient conditions for optimality.…
The optimal constants in a class of exponential type inequalities for the Ornstein-Uhlenbeck operator in the Gauss space are detected. The existence of extremal functions in the relevant inequalities is also established. Our results…
We prove that optimal strategies exist in every perfect-information stochastic game with finitely many states and actions and a tail winning condition.
The goal of this paper is to investigate the minimisation of the first eigenvalue of the (vectorial) incompressible Dirichlet-Stokes operator. After providing an existence result, we investigate optimality conditions and we prove the…
We consider sequences-indexed by time (discrete stages)-of families of multistage stochastic optimization problems. At each time, the optimization problems in a family are parameterized by some quantities (initial states, constraint…
We consider a quasi-variational inequality governed by a moving set. We employ the assumption that the movement of the set has a small Lipschitz constant. Under this requirement, we show that the quasi-variational inequality has a unique…
In the first part of the note we prove that a sufficient condition (due to Simons) for the convexity of the closure of the domain/range of a monotone operator is also necessary when the operator has bounded domain and is maximal. Simons'…
A symmetrization inequality of Rogers and of Brascamp-Lieb-Luttinger states that for a certain class of multilinear integral expressions, among tuples of sets of prescribed Lebesgue measures, tuples of balls centered at the origin are among…
In this paper we study some improvements of the classical Hardy inequality. We add to the right hand side of the inequality a term which depends on some Lorentz norms of $u$ or of its gradient and we find the best values of the constants…
Necessary and sufficient conditions for the existence of a composite-system statistical operator, and, separately, for the possibility of its being correlated or uncorrelated, are derived in terms of its range dimension and the range…
We consider the best constant in a critical Sobolev inequality of second order. We show non-rigidity for the optimizers above a certain threshold, namely we prove that the best constant is achieved by a non-constant solution of the…
In this article we show how ideas, methods and results from optimal transportation can be used to study various aspects of the stationary measuresof Iterated Function Systems equipped with a probability distribution. We recover a classical…
The aim of this article is to give some improvements of Jordan-Steckin and Becker-Stark inequalities discussed in [1].
In this note besides two abstract versions of the Vitali Covering Lemma an abstract Hardy-Littlewood Maximal Inequality, generalizing weak type (1,1) maximal function inequality, associated to any outer measure and a family of subsets on a…
We study autocorrelation inequalities, in the spirit of Barnard and Steinerberger's work. In particular, we obtain improvements on the sharp constants in some of the inequalities previously considered by these authors, and also prove…
We study the problem of minimizing the second Dirichlet eigenvalue for the Laplacian operator among sets of given perimeter. In two dimensions, we prove that the optimum exists, is convex, regular, and its boundary contains exactly two…