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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.11976 |
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| _version_ | 1866914558150443008 |
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| author | Recke, Lutz |
| author_facet | Recke, Lutz |
| contents | We consider homogenization of Dirichlet problems for semilinear elliptic systems with non-smooth data. We suppose that the diffusion tensors H-converge if the homogenization parameter tends to zero. Our result is of implicit function theorem type: For small homogenization parameter there exists exactly one weak solution close to a given non-degenerate weak solution to the homogenized problem. For the proofs we use gradient estimates of Meyers (if the space dimension is two) or Morrey (if the diffusion tensors are triangular) type for solutions to linear elliptic systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_11976 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An H-convergence-based implicit function theorem for homogenization of nonlinear non-smooth elliptic systems Recke, Lutz Analysis of PDEs 35B27 35D30 35J57 35J61 35R05 47J07 We consider homogenization of Dirichlet problems for semilinear elliptic systems with non-smooth data. We suppose that the diffusion tensors H-converge if the homogenization parameter tends to zero. Our result is of implicit function theorem type: For small homogenization parameter there exists exactly one weak solution close to a given non-degenerate weak solution to the homogenized problem. For the proofs we use gradient estimates of Meyers (if the space dimension is two) or Morrey (if the diffusion tensors are triangular) type for solutions to linear elliptic systems. |
| title | An H-convergence-based implicit function theorem for homogenization of nonlinear non-smooth elliptic systems |
| topic | Analysis of PDEs 35B27 35D30 35J57 35J61 35R05 47J07 |
| url | https://arxiv.org/abs/2605.11976 |