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Joel Fotso Tachago

Publications and source records attributed to Joel Fotso Tachago.

16 recordsLinked to original sources
arXiv2026

Surface-to-Volume Homogenization of NonLinear Steklov Eigencouples with NonHomogeneous Orlicz Growth in Perforated Domains

We study normalized principal Steklov eigencouples on periodically perforated domains when both the bulk energy and the boundary normalization have general, possibly nonhomogeneous, Orlicz growth. The surface term on the hole boundaries carries the critical surface-to-volume scaling. For each fixed mass level, the constrained minima converge along the whole family, while selected minimizers, fluxes and Lagrange multipliers converge along subsequences to the corresponding objects of a homogenized problem. In the limit, the bulk operator is given by a convex cell problem, and the boundary term becomes a volume term weighted by the total surface density of the reference hole. The key tool is a strong approximation of the microscopic traces by cell averages, measured in the scaled surface modular.

math.AP↗
arXiv2026

Stochastic $Σ$-convergence in Orlicz setting and Applications

This paper aims to extend the concept of stochastic $Σ$-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 $Σ$-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↗
arXiv2026

Homogenization and integral representation of energy functionals in manifold valued Orlicz-Sobolev spaces

This paper aims to extend to Orlicz-Sobolev spaces some results of integral representation for the simultaneous homogenization and dimensional reduction of integral energies defined on fields taking values on a differentiable manifold. Since our functional framework goes beyond the classical Sobolev's spaces, we also prove, via $Γ$-convergence, a general integral representation results in the unconstrained Orlicz setting. Due to $Δ_2$ and $\nabla_2$ conditions verified by the Young function $Φ$ (which modulated the growth behaviour), we prove that the density of the $Γ$-limit is a tangential quasiconvex integrand represented by a cell formula.

math.AP↗
arXiv2025

Reiterated $Σ$-Convergence In Orlicz Setting and Applications

The concept of reiterated $Σ$-convergence (and more generally of multiscale $Σ$-convergence) is extended to framework of Orlicz-Sobolev spaces, in order to deals with homogenization of multiscales problems in general deterministic setting and whose solutions leads in this type of spaces. This concept relies on the notion of reiterated homogenization supralgebra that we will assumed being ergodic. An application to the deterministic reiterated homogenization of nonlinear degenerate elliptic operators with nonstandard growth is given and some concrete homogenization problems following varied structure hypothesis are deduce from this latter.

math.AP↗
arXiv2025

Stochastic two-scale convergence in the mean in Orlicz-Sobolev's spaces and applications to the homogenization of an integral functional

In this paper, we study the stochastic homogenization for a family of integral functionals with convex and nonstandard growth integrands defined on Orlicz-Sobolev's spaces. One fundamental in this topic is to extend the classical compactness results of the two-scale convergence in the mean method to this type of spaces. Moreover, it is shown by the two-scale convergence in the mean 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.AP↗
arXiv2024

Reiterated Periodic Homogenization of Parabolic Monotone Operators with Nonstandard Growth

In this paper, we are interested in reiterated periodic homogenization for a family of parabolic problems with nonstandard growth monotone operators leading to Orlicz spaces. The aim of this work is the determination of the global homogenized problem on the one hand and the macroscopic homogenized problem on the other hand, via the reiterated two-scale convergence method adapted to this type of spaces.

math.AP↗
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↗