arXiv subjects

Franck Tchinda

Publications and source records attributed to Franck Tchinda.

5 recordsLinked to original sources

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

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

Stochastic-periodic homogenization of Poisson-Nernst-Planck equations in porous media

This paper is devoted to the study of the stochastic-periodic homogenization of Poisson-Nernst-Planck equations in porous media. It is shown by the stochastic two-scale convergence method extended to periodic surfaces that results in a global homogenized problem having suitable coefficients.

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↗

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↗