Homogenization and integral representation of energy functionals in manifold valued Orlicz-Sobolev spaces
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917409612365824 |
|---|---|
| author | Dongho, Joseph Tachago, Joel Fotso Tchinda, Franck Zappale, Elvira |
| author_facet | Dongho, Joseph Tachago, Joel Fotso Tchinda, Franck Zappale, Elvira |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_13498 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Homogenization and integral representation of energy functionals in manifold valued Orlicz-Sobolev spaces Dongho, Joseph Tachago, Joel Fotso Tchinda, Franck Zappale, Elvira Analysis of PDEs 74Q05, 49J45, 49Q20, 78A99, 28A33, 46E30 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. |
| title | Homogenization and integral representation of energy functionals in manifold valued Orlicz-Sobolev spaces |
| topic | Analysis of PDEs 74Q05, 49J45, 49Q20, 78A99, 28A33, 46E30 |
| url | https://arxiv.org/abs/2604.13498 |