Stochastic two-scale convergence in the mean in Orlicz-Sobolev's spaces and applications to the homogenization of an integral functional
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| Format: | Preprint |
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2023
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| _version_ | 1866915384279433216 |
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| author | Dongho, Joseph Tachago, Joel Fotso Tchinda, Franck |
| author_facet | Dongho, Joseph Tachago, Joel Fotso Tchinda, Franck |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_13202 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stochastic two-scale convergence in the mean in Orlicz-Sobolev's spaces and applications to the homogenization of an integral functional Dongho, Joseph Tachago, Joel Fotso Tchinda, Franck Analysis of PDEs Probability 35B27, 35J20, 46E30, 37A05 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. |
| title | Stochastic two-scale convergence in the mean in Orlicz-Sobolev's spaces and applications to the homogenization of an integral functional |
| topic | Analysis of PDEs Probability 35B27, 35J20, 46E30, 37A05 |
| url | https://arxiv.org/abs/2310.13202 |