Stochastic $Σ$-convergence in Orlicz setting and Applications
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| Format: | Preprint |
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2026
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| _version_ | 1866910153122512896 |
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| author | Tachago, Joel Fotso Nnang, Hubert Takougoum, Franck Tchinda Woukeng, Jean Louis |
| author_facet | Tachago, Joel Fotso Nnang, Hubert Takougoum, Franck Tchinda Woukeng, Jean Louis |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_19200 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stochastic $Σ$-convergence in Orlicz setting and Applications Tachago, Joel Fotso Nnang, Hubert Takougoum, Franck Tchinda Woukeng, Jean Louis Probability Analysis of PDEs 35B40, 37A55, 46E30, 46J10, 49J55 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. |
| title | Stochastic $Σ$-convergence in Orlicz setting and Applications |
| topic | Probability Analysis of PDEs 35B40, 37A55, 46E30, 46J10, 49J55 |
| url | https://arxiv.org/abs/2604.19200 |