Related papers: Green function and invariant measure estimates for…
We study the qualitative homogenization of second order viscous Hamilton-Jacobi equations in space-time stationary ergodic random environments. Assuming that the Hamiltonian is convex and superquadratic in the momentum variable (gradient)…
The main aspects of a gauge-invariant approach to the description of quark dynamics in the nonperturbative regime of QCD are first reviewed. In particular, the role of the parallel transport operation in constructing gauge-invariant Green's…
We study the Green function for the stationary Stokes system with bounded measurable coefficients in a bounded Lipschitz domain $\Omega\subset \mathbb{R}^n$, $n\ge 3$. We construct the Green function in $\Omega$ under the condition…
We study the large scale behavior of elliptic systems with stationary random coefficient that have only slowly decaying correlations. To this aim we analyze the so-called corrector equation, a degenerate elliptic equation posed in the…
This introduction to Green's functions is based on their role as kernels of differential equations. The procedures to construct solutions to a differential equation with an external source or with an inhomogeneity term are put together to…
It is shown that the Lorentz transformations can be derived for a non-orthogonal Euclidean space. In this geometry one finds the same relations of special relativity as the ones known from the orthogonal Minkowski space. In order to…
We establish a new type of local asymptotic formula for the Green's function ${\mathcal G}_t(x,y)$ of a uniformly parabolic linear operator $\partial_t - L$ with non-constant coefficients using dilations and Taylor expansions at a point…
We study relations and characterizations of various elliptic Harnack inequalities for symmetric non-local Dirichlet forms on metric measure spaces. We allow the scaling function be state-dependent and the state space possibly disconnected.…
We obtain new partial H\"older continuity results for solutions to divergence form elliptic systems with discontinuous coefficients, obeying $p(x)$-type nonstandard growth conditions. By an application of the method of…
The equilibration of two coupled reservoirs is studied using a Green function approach which is suitable for future development with the closed time path method. The problem is solved in two parameterizations, in order to demonstrate the…
Many important properties of granular fluids can be represented by a system of hard spheres with inelastic collisions. Traditional methods of nonequilibrium statistical mechanics are effective for analysis and description of the inelastic…
Field-theoretic construction of functional representations of solutions of stochastic differential equations and master equations is reviewed. A generic expression for the generating function of Green functions of stochastic systems is put…
We establish uniform Lipschitz estimates for second-order elliptic systems in divergence form with rapidly oscillating, almost-periodic coefficients. We give interior estimates as well as estimates up to the boundary in bounded…
The aim of this paper is twofold. The first is to study the asymptotics of a parabolically scaled, continuous and space-time stationary in time version of the well-known Funaki-Spohn model in Statistical Physics. After a change of unknowns…
In a companion article we have introduced a notion of multiscale functional inequalities for functions $X(A)$ of an ergodic stationary random field $A$ on the ambient space $\mathbb R^d$. These inequalities are multiscale weighted versions…
The disorder averaged single-particle Green's function of electrons subject to a time-dependent random potential with long-range spatial correlations is calculated by means of bosonization in arbitrary dimensions. For static disorder our…
Based on an assumption on the Hessian of the Green function, we derive some monotonicity formulas on nonparabolic manifolds. This assumption is satisfied on manifolds that meet certain conditions including bounds on the sectional curvature…
This article is concerned with numerical methods to approximate effective coefficients in stochastic homogenization of discrete linear elliptic equations, and their numerical analysis --- which has been made possible by recent contributions…
Parameters of differential equations are essential to characterize intrinsic behaviors of dynamic systems. Numerous methods for estimating parameters in dynamic systems are computationally and/or statistically inadequate, especially for…
We establish an optimal, linear rate of convergence for the stochastic homogenization of discrete linear elliptic equations. We consider the model problem of independent and identically distributed coefficients on a discretized unit torus.…