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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 requiring the existence of a space-time stationary eternal solution of a stochastically perturbed heat equation, the problem transforms to the qualitative homogenization of a uniformly elliptic, space-time stationary, divergence form, nonlinear partial differential equation, the study of which is the second aim of the paper. An important step is the construction of correctors with the appropriate behavior at infinity.
We derive optimal-order homogenization rates for random nonlinear elliptic PDEs with monotone nonlinearity in the uniformly elliptic case. More precisely, for a random monotone operator on $mathbb{R}^d$ with stationary law (i.e. spatially homogeneous
Let $ngeq 3$, $0le m<frac{n-2}{n}$, $rho_1>0$, $beta>beta_0^{(m)}=frac{mrho_1}{n-2-nm}$, $alpha_m=frac{2beta+rho_1}{1-m}$ and $alpha=2beta+rho_1$. For any $lambda>0$, we prove the uniqueness of radially symmetric solution $v^{(m)}$ of $La(v^m/m)+alph
Corrector estimates constitute a key ingredient in the derivation of optimal convergence rates via two-scale expansion techniques in homogenization theory of random uniformly elliptic equations. The present work follows up - in terms of corrector est
Let $(Omega, mu)$ be a probability space endowed with an ergodic action, $tau$ of $( {mathbb R} ^n, +)$. Let $H(x,p; omega)=H_omega(x,p)$ be a smooth Hamiltonian on $T^* {mathbb R} ^n$ parametrized by $omegain Omega$ and such that $ H(a+x,p;tau_aomeg
In this paper we characterize viscosity solutions to nonlinear parabolic equations (including parabolic Monge-Amp`ere equations) by asymptotic mean value formulas. Our asymptotic mean value formulas can be interpreted from a probabilistic point of vi