Related papers: A Poincar\'e cone condition in the Poincar\'e grou…
We consider a particle transport process in a one-dimensional system with a thin membrane, described by a normal diffusion equation. We consider two boundary conditions at the membrane that are linear combinations of integral operators,…
We give general conditions for the central limit theorem and weak convergence to Brownian motion (the weak invariance principle / functional central limit theorem) to hold for observables of compact group extensions of nonuniformly…
Starting with the Green's functions found for normal diffusion, we construct exact time-dependent Green's functions for subdiffusive equation (with fractional time derivatives), with the boundary conditions involving a linear combination of…
This paper presents an extended version of the article [Franz, S., Kopteva, N.: J. Differential Equations, 252 (2012)]. The main improvement compared to the latter is in that here we additionally estimate the mixed second-order derivative…
We obtain a generalization of the relativistic diffusion of Schay and Dudley for particles with spin. The diffusion equation is a classical version of an equation for the Wigner function of an elementary particle. The elementary particle is…
This paper is concerned with the study of Green's functions for one dimensional diffusions with constant diffusion coefficient and linear time inhomogeneous drift. It is well know that the whole line Green's function is given by a Gaussian.…
The Neumann boundary problem for the perturbed sine-Gordon equation describing the electrodynamics of Josephson junctions has been considered. The behavior of a viscous term, described by a higher-order derivative with small diffusion…
We extend the directional Poincar\'e inequality on the torus, introduced by Steinerberger in [Ark. Mat. 54 (2016), pp. 555--569], to the setting of compact Lie groups. We provide necessary and sufficient conditions for the existence of such…
In the setting of multidimensional diffusions in random environment, we carry on the investigation of condition $(T')$, introduced by Sznitman [Ann. Probab. 29 (2001) 723--764] and by Schmitz [Ann. Inst. H. Poincar\'{e} Probab. Statist. 42…
Consider a discrete uniformly elliptic divergence form equation on the $d$ dimensional lattice $\Z^d$ with random coefficients. In [3] rate of convergence results in homogenization and estimates on the difference between the averaged…
We prove a new type of Poincar\'e inequality on abstract Wiener spaces for a family of probability measures which are absolutely continuous with respect to the reference Gaussian measure. This class of probability measures is characterized…
We present a new interpretation for reduced density matrices of secondary variables in relativistic systems via an analysis of Wigner's method to construct the irreducible unitary representations of the Poincar\'e group. We argue that the…
The Poincar\'{e}-Bendixson theorem is one of the most fundamental tools to capture the limit behaviors of orbits of flows. It was generalized and applied to various phenomena in dynamical systems, differential equations, foliations, group…
The goal of this paper is to give a non-local sufficient condition for generalized Poincar\'e inequalities, which extends the well-known Bakry-Emery condition. Such generalized Poincar\'e inequalities have been introduced by W. Beckner in…
A theoretical study on the weak scattering formulation for flexural waves in thin elastic plates loaded by point-like resonators is reported. Our approach employs the Born approximation and far-field asymptotics of the Green function to…
We obtain and study new $\Phi$-entropy inequalities for diffusion semigroups, with Poincar\'e or logarithmic Sobolev inequalities as particular cases. From this study we derive the asymptotic behaviour of a large class of linear…
Working on the approximation of low frequency, we present the light cone conditions for a class of theories constructed with the two gauge invariants of the Maxwell field without making use of average over polarization states. Different…
A linear singularly perturbed convection-diffusion problem with characteristic layers is considered in three dimensions. Sharp bounds for the associated Green's function and its derivatives are established in the $L_1$ norm. The dependence…
As a continuation to \cite{MRW} where the Poincar\'e and log-Sobolev inequalities were studied for the sticky-reflected Brownian motion on Riemannian manifolds with boundary, this paper establishes the super and weak Poincar\'e inequalities…
We consider elliptic operators in divergence form with lower order terms of the form $Lu=-$div$\nabla u+bu)-c\nabla u-du$, in an open set $\Omega\subset \mathbb{R}^n$, $n\geq 3$, with possibly infinite Lebesgue measure. We assume that the…