Regularity theorems for random elliptic operators on domains
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911560524365824 |
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| author | Bella, Peter Fischer, Julian Josien, Marc Raithel, Claudia |
| author_facet | Bella, Peter Fischer, Julian Josien, Marc Raithel, Claudia |
| contents | Regularity theorems à la Avellaneda-Lin are an indispensable part of the modern quantitative theory of stochastic homogenization. While interior regularity results for random elliptic operators have been available for a while, on general smooth domains the existing theory has until recently remained limited to Lipschitz estimates. We establish $C^{1,α}$ regularity results for random elliptic operators on bounded sufficiently smooth domains, as well as for scalar problems on convex polytopes. We, furthermore, prove a number of auxiliary results typically employed in the derivation of fluctuation bounds, such as a weighted Meyers estimate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_01209 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Regularity theorems for random elliptic operators on domains Bella, Peter Fischer, Julian Josien, Marc Raithel, Claudia Analysis of PDEs 35J25, 60K37, 60H25 Regularity theorems à la Avellaneda-Lin are an indispensable part of the modern quantitative theory of stochastic homogenization. While interior regularity results for random elliptic operators have been available for a while, on general smooth domains the existing theory has until recently remained limited to Lipschitz estimates. We establish $C^{1,α}$ regularity results for random elliptic operators on bounded sufficiently smooth domains, as well as for scalar problems on convex polytopes. We, furthermore, prove a number of auxiliary results typically employed in the derivation of fluctuation bounds, such as a weighted Meyers estimate. |
| title | Regularity theorems for random elliptic operators on domains |
| topic | Analysis of PDEs 35J25, 60K37, 60H25 |
| url | https://arxiv.org/abs/2604.01209 |