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Related papers: Behaviour of the Brascamp--Lieb constant

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We study a reaction-diffusion equation with a nonlocal reaction term that models a population with variable motility. We establish a global supremum bound for solutions of the equation. We investigate the asymptotic (long-time and…

Analysis of PDEs · Mathematics 2016-03-07 Olga Turanova

H\"older-Brascamp-Lieb inequalities provide upper bounds for a class of multilinear expressions, in terms of $L^p$ norms of the functions involved. They have been extensively studied for functions defined on Euclidean spaces.…

Classical Analysis and ODEs · Mathematics 2015-10-15 Michael Christ , James Demmel , Nicholas Knight , Thomas Scanlon , Katherine Yelick

The paper deals with a nonlinear evolution equation describing the dynamics of a non homogeneous multiply hinged beam, subject to a nonlocal restoring force of displacement type. First, a spectral analysis for the associated weighted…

Analysis of PDEs · Mathematics 2020-10-21 E. Berchio , A. Falocchi , M. Garrione

In this short paper we provide a new proof of the geometric Forward-Reverse Brascamp-Lieb inequality, using the approach of the heat semigroup, or the heat flow. Furthermore, we characterize all the Forward-Reverse Brascamp-Lieb data such…

Analysis of PDEs · Mathematics 2026-04-24 Ye Zhang

Given any (forward) Brascamp--Lieb inequality on euclidean space, a famous theorem of Lieb guarantees that gaussian near-maximizers always exist. Recently, Barthe and Wolff used mass transportation techniques to establish a counterpart to…

Classical Analysis and ODEs · Mathematics 2025-06-18 Neal Bez , Shohei Nakamura

We present a regularized version of H\"{o}lder-Brascamp-Lieb inequalities studied by Bennett, Carbery, Christ, and Tao. These inequalities lead to a generalization of the multilinear Kakeya inequality.

Classical Analysis and ODEs · Mathematics 2021-02-08 Dominique Maldague

We study stability of the sharp Poincar{\'e} constant of the invariant probability measure of a reversible diffusion process satisfying some natural conditions. The proof is based on the spectral interpretation of Poincar{\'e} inequalities…

Classical Analysis and ODEs · Mathematics 2022-02-04 Jordan Serres

The H\"older-Brascamp-Lieb inequalities are a collection of multilinear inequalities generalizing a convolution inequality of Young and the Loomis-Whitney inequalities. The full range of exponents was classified in Bennett et al. (2008). In…

Classical Analysis and ODEs · Mathematics 2017-11-23 Kevin O'Neill

Under some assumptions on the vectors $a_{1},..,a_{n} \in\mathbb{R}^{k}$ and the function $B : \mathbb{R}^{n} \to \mathbb{R}$ we find the sharp estimate of the expression $\int_{\mathbb{R}^{k}} B(u_{1}(a_{1}\cdot x),..., u_{n}(a_{n}\cdot…

Analysis of PDEs · Mathematics 2017-05-17 P. Ivanisvili , A. Volberg

Human heart rate fluctuates in a complex and non-stationary manner. Elaborating efficient and adequate tools for the analysis of such signals has been a great challenge for the researchers during last decades. Here, an overview of the main…

Medical Physics · Physics 2007-05-23 J. Kalda , M. Sakki , M. Vainu , M. Laan

We obtain global and local theorems on the existence of invariant manifolds for perturbations of non autonomous linear difference equations assuming a very general form of dichotomic behavior for the linear equation. The results obtained…

Dynamical Systems · Mathematics 2012-10-01 António J. G. Bento , César M. Silva

The Brascamp-Lieb inequalities are a generalization of the H\"older, Loomis-Whitney, Young, and Finner inequalities that have found many applications in harmonic analysis and elsewhere. In this paper we introduce an "adjoint" version of…

Classical Analysis and ODEs · Mathematics 2023-07-18 Jonathan Bennett , Terence Tao

Abstract H\"{o}lder-Brascamp-Lieb inequalities have become a ubiquitous tool in Fourier analysis in recent years, due in large part to a theorem of Bennett, Carbery, Christ, and Tao (2008,2010) characterizing finiteness of the…

Classical Analysis and ODEs · Mathematics 2025-03-21 Philip T. Gressman

For a general class of translationally invariant systems with a specific category of nonlinearity in the output, this paper presents necessary and sufficient conditions for global observability. Critically, this class of systems cannot be…

Dynamical Systems · Mathematics 2022-10-11 Eduardo D. Sontag , Debojyoti Biswas , Noah J. Cowan

We consider a model system of persistent random walkers that can jam, pass through each other or jump apart (recoil) on contact. In a continuum limit, where particle motion between stochastic changes in direction becomes deterministic, we…

Statistical Mechanics · Physics 2023-05-03 Matthew J Metson , Martin R Evans , Richard A Blythe

Brascamp-Lieb inequalities are entropy inequalities which have a dual formulation as generalized Young inequalities. In this work, we introduce a fully quantum version of this duality, relating quantum relative entropy inequalities to…

Quantum Physics · Physics 2023-03-17 Mario Berta , David Sutter , Michael Walter

In this article, we derive a new covariance estimate. The estimate has a similar structure as the Brascamp-Lieb inequality and is optimal for ferromagnetic Gaussian measures. It can be naturally applied to deduce decay of correlations of…

Probability · Mathematics 2014-02-24 Georg Menz

We prove the full range of estimates for a five-linear singular integral of Brascamp-Lieb type. The study is methodology-oriented with the goal to develop a sufficiently general technique to estimate singular integral variants of…

Classical Analysis and ODEs · Mathematics 2022-09-14 Camil Muscalu , Yujia Zhai

We study lower bounds on multilinear operators with Gaussian kernels acting on Lebesgue spaces, with exponents below one. We put forward natural conditions when the optimal constant can be computed by inspecting centered Gaussian functions…

Functional Analysis · Mathematics 2018-05-08 Franck Barthe , Pawel Wolff

A simple general theorem is used as a tool that generates nonlocal constants of motion for Lagrangian systems. We review some cases where the constants that we find are useful in the study of the systems: the homogeneous potentials of…

Dynamical Systems · Mathematics 2020-09-28 Gianluca Gorni , Gaetano Zampieri