Related papers: Nonlinear stochastic homogenization in Orlicz spac…

In this article we prove modular and norm P\'olya-Szeg\"o inequalities in general fractional Orlicz-Sobolev spaces by using the polarization technique. We introduce a general framework which includes the different definitions of theses…

In this note we extend to the random, stationary ergodic setting previous results of periodic homogenization for a particular family of nonlinear nonlocal "elliptic" equations with oscillatory coefficients. Such equations include, but are…

This paper is concerned with the behavior of the homogenized coefficients associated with some random stationary ergodic medium under a Bernoulli perturbation. Introducing a new family of energy estimates that combine probability and…

$\Gamma$-convergence methods are used to prove homogenization results for fractional obstacle problems in periodically perforated domains. The obstacles have random sizes and shapes and their capacity scales according to a stationary…

In this paper we extend the homogenization results obtained in (G. Allaire, A. Mikeli\'c, A. Piatnitski, J. Math. Phys. 51 (2010), 123103) for a system of partial differential equations describing the transport of a N-component electrolyte…

With recently developed tools, we prove a homogenisation theorem for a random ODE with short and long-range dependent fractional noise. The effective dynamics are not necessarily diffusions, they are given by stochastic differential…

This article establishes an algebraic error estimate for the stochastic homogenization of fully nonlinear uniformly parabolic equations in stationary ergodic spatio-temporal media. The approach is similar to that of Armstrong and Smart in…

Certain inequalities between the values of the modular and the norm in the Orlicz spaces are established. These inequalities are applied then to the theory of solvability of nonlinear integral equations of Hammerstein type.

We define Euler-Hilbert-Sobolev spaces and obtain embedding results on homogeneous groups using Euler operators, which are homogeneous differential operators of order zero. Sharp remainder terms of $L^{p}$ and weighted Sobolev type and…

We study the stochastic homogenization of the system -div \sigma^\epsilon = f^\epsilon \sigma^\epsilon \in \partial \phi^\epsilon (\nabla u^\epsilon), where (\phi^\epsilon) is a sequence of convex stationary random fields, with p-growth. We…

The objective is to investigate the global existence of solutions for a degenerate chemotaxis system with logistic sources in a two-dimensional domain. It is demonstrated that the inclusion of logistic sources can exclude the occurrence of…

For a semifinite von Neumann algebra M, individual convergence of subsequential, \mathcal{Z}(M) (center of M) valued weighted ergodic averages are studied in noncommutative Orlicz spaces. In the process, we also derive a maximal ergodic…

We consider a nonlinear drift-diffusion system for multiple charged species in a porous medium in 2D and 3D with periodic microstructure. The system consists of a transport equation for the concentration of the species and Poisson's…

We consider random fields indexed by finite subsets of an amenable discrete group, taking values in the Banach-space of bounded right-continuous functions. The field is assumed to be equivariant, local, coordinate-wise monotone, and almost…

We prove a version of the negative norm theorem in Orlicz-Sobolev spaces. A study of continuity properties of the Bogovskii -operator between Orlicz spaces is a crucial step, of independent interest, in our approach. Applications to the…

In this paper we introduce and exploit the real replica approach for a minimal generalization of the Hopfield model, by assuming the learned patterns to be distributed accordingly to a standard unit Gaussian. We consider the high storage…

In earlier papers Poisson equation in the whole space was studied for so called ergodic generators $L$ corresponding to homogeneous Markov diffusions ($X_t, \, t\ge 0$) in $\mathbb R^d$. Solving this equation is one of the main tools for…

We investigate the homogenization of inclusions of infinite conductivity, randomly stationary distributed inside a homogeneous conducting medium. A now classical result by Zhikov shows that, under a logarithmic moment bound on the…

The optimal Orlicz target space is exhibited for embeddings of fractional-order Orlicz-Sobolev spaces in $\mathbb R^n$. An improved embedding with an Orlicz-Lorentz target space, which is optimal in the broader class of all…

We give a general method of deriving statistical limit theorems, such as the central limit theorem and its functional version, in the setting of ergodic measure preserving transformations. This method is applicable in situations where the…