arXiv subjects

Hubert Nnang

Publications and source records attributed to Hubert Nnang.

9 recordsLinked to original sources

arXiv2026

Stochastic $\Sigma$-convergence in Orlicz setting and Applications

This paper aims to extend the concept of stochastic $\Sigma$-convergence to the framework of Orlicz-Sobolev spaces in order to deals with coupled stochastic and deterministic homogenization problems in this type of spaces. Thus, this concept is a combination of both well-known $\Sigma$-convergence [\textit{Acta Math. Sinica, English Series} \textbf{30}(9) 1621-1654] and stochastic two-scale convergence in the mean schemes [\textit{Asympt. Anal. (2025)} \textbf{142}, 291-320]. An application to the stochastic-deterministic homogenization (in the context of ergodic $H$-supralgebra) of a class of highly oscillatory minimizations problems involving integral functionals with convex and nonstandard growth integrands is also given, and some concrete homogenization problems following varied structure hypothesis are deduce from this latter.

math.PR↗

arXiv2024

Homogenization of non-convex integral energies with Orlicz growth via periodic unfolding

The periodic unfolding method is extended to the Orlicz setting and used to prove a homogenization result for non-convex integral energies defined on vector-valued configurations in the Orlicz-Sobolev setting.

math.AP↗

arXiv2024

(Two-scale) $W^{1}L^Φ$-gradient Young measures and homogenization of integral functionals in Orlicz-Sobolev spaces

(Two-scale) gradient Young measures in Orlicz-Sobolev setting are introduced and characterized providing also an integral representation formula for non convex energies arising in homogenization problems with nonstandard growth.

math.AP↗

arXiv2023

Stochastic-Periodic homogenization of Maxwell's equations with nonlinear and periodic conductivity

Stochastic-periodic homogenization is studied for the Maxwell equations with nonlinear and periodic electric conductivity. It is shown by the stochastic-two-scale convergence method that the sequence of solutions of a class of highly oscillatory problems converges to the solution of a homogenized Maxwell equation.

math.AP↗

arXiv2023

Reiterated Homogenization of nonlinear degenerate elliptic operators with nonstandard growth

It is shown by means of reiterated two-scale convergence in the Sobolev-Orlicz setting, that the sequence of solutions of a class of highly oscillatory problems involving nonlinear elliptic operators with nonstandard growth, converges to a solution of a suitable homogeneous nonlinear elliptic equation associated to an operator with nonstandard growth.

math.AP↗

arXiv2023

Some convergence results on the periodic Unfolding Operator in Orlicz setting

The aim of this note consists of the introduction of unfolding operator in the Orlicz setting.

math.AP↗

arXiv2020

Reiterated periodic homogenization of integral functionals with convex and nonstandard growth integrands

Multiscale periodic homogenization is extended to an Orlicz-Sobolev setting. It is shown by the reiteraded periodic two-scale convergence method that the sequence of minimizers of a class of highly oscillatory minimizations problems involving convex functionals, converges to the minimizers of a homogenized problem with a suitable convex function.

math.OC↗

arXiv2019

Multiscale homogenization of integral convex functionals in Orlicz Sobolev setting

The $Γ$-limit of a family of functionals $u\mapsto \int_{Ω}f\left( \frac{x}{\varepsilon },\frac{x}{\varepsilon ^{2}},D^{s}u\right) dx$ is obtained for $s=1,2$ and when the integrand $f=f\left( y,z,v\right) $ is a continous function, periodic in $y$ and $z$ and convex with respect to $v$ with nonstandard growth. The reiterated two-scale limits of second order derivative are characterized in this setting.

math.OC↗

arXiv2018

Relaxation of Periodic and Nonstandard Growth Integrals by means of Two-scale convergence

An integral representation result is obtained for the variational limit of the family functionals $\int_Ωf\left(\frac{x}{\varepsilon}, Du\right)dx$, as $\varepsilon \to 0$, when the integrand $f = f (x,v)$ is a Carathéodory function, periodic in $x$, convex in $v$ and with nonstandard growth.

math.AP↗