相关论文: A parabolic PDE-based approach to Borell--Brascamp…

We study a second-order parabolic equation with divergence form elliptic operator, having piecewise constant diffusion coefficients with two points of discontinuity. Such partial differential equations appear in the modelization of…

This paper is concerned with lattice field models in dimension at least 2. The action is a uniformly convex function of the gradient of the field. The main result Theorem 1.4 proves that charge-charge correlations in the Coulomb dipole gas…

In this work, we study the Sobolev inequality on noncommutative Euclidean spaces. As a simple consequence, we obtain the Gagliardo-Nirenberg type inequality and as its application we show global well-posedness of nonlinear PDEs in the…

It was observed recently in work of Bez, Buschenhenke, Cowling, Flock and the first author, that the euclidean Brascamp-Lieb inequality satisfies a natural and useful Fourier duality property. The purpose of this paper is to establish an…

This paper is devoted to the study of some nonlinear parabolic equations with discontinuous diffusion intensities. Such problems appear naturally in physical and biological models. Our analysis is based on variational techniques and in…

A degenerate fourth-order parabolic equation modeling condensation phenomena related to Bose-Einstein particles is analyzed. The model is a Fokker-Planck-type approximation of the Boltzmann-Nordheim equation, only keeping the leading order…

In this paper, we are interested in Gaussian versions of the classical Brunn-Minkowski inequality. We prove in a streamlined way a semigroup version of the Ehrard inequality for $m$ Borel or convex sets based on a previous work by Borell.…

In this paper, we prove a Pr\'ekopa-Leindler type inequality of the $L_p$ Brunn-Minkowski inequality. It extends an inequality proved by Das Gupta [8] and Klartag [16], and thus recovers the Pr\'ekopa-Leindler inequality. In addition, we…

We derive the partial differential equation (PDE) to which the pseudo-potential lattice Boltzmann method (P-LBM) converges under diffusive scaling, providing a rigorous basis for its consistency analysis. By establishing a direct link…

We propose a new mathematical model of groundwater flow in porous medium layered over inclined impermeable bed. In its full generality, this is a free-surface problem. To obtain analytically tractable model, we use generalized…

In 2011 Lutwak, Yang and Zhang extended the definition of the $L_p$-Minkowski convex combination ($p \geq 1$) introduced by Firey in the 1960s from convex bodies containing the origin in their interiors to all measurable subsets in…

In this article, a proof of the interpolation inequality along geodesics in $p$-Wasserstein spaces is given. This interpolation inequality was the main ingredient to prove the Borel-Brascamp-Lieb inequality for general Riemannian and…

The paper considers parabolic equations in non-divergent form with discontinuous coefficients at higher derivatives. Their investigation is most complicated because, in general, in the case of discontinuous coefficients, the uniqueness of a…

We prove an $L^2$-stability estimate for the variance Brascamp-Lieb inequality [J. Funct. Anal. 22 (4), 366-389 (1976)] by bootstrapping the recent $L^1$-stability theorem of Machado and Ramos [arXiv:2511.22636] under an additional…

Biot's equations of poroelasticity contain a parabolic system for the evolution of the pressure, which is coupled with a quasi-stationary equation for the stress tensor. Thus, it is natural to extend the existing work on isogeometric…

A new proof is given for the fact that centered gaussian functions saturate the Euclidean forward-reverse Brascamp-Lieb inequalities, extending the Brascamp-Lieb and Barthe theorems. A duality principle for best constants is also developed,…

We present the bilinear forms of the (continuous) Painlev\'e equations obtained from the continuous limit of the analogous expresssions for the discrete ones. The advantage of this method is that it leads to very symmetrical results. A new…

We use the results of ultra-precise cold-atom-recoil experiments to constrain the form of the energy-momentum dispersion relation, a structure that is expected to be modified in several quantum-gravity approaches. Our strategy of analysis…

We show the continuous dependence of solutions of linear nonautonomous second order parabolic partial differential equations (PDEs) with bounded delay on coefficients and delay. The assumptions are very weak: only convergence in the weak-*…

Pseudo-parabolic equations have been used to model unsaturated fluid flow in porous media. In this paper it is shown how a pseudo-parabolic equation can be upscaled when using a spatio-temporal decomposition employed in the…