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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2510.15249 |
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| _version_ | 1866909852438102016 |
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| author | Abdulla, Ugur G. Brazke, Denis |
| author_facet | Abdulla, Ugur G. Brazke, Denis |
| contents | This paper establishes a Wiener criterion at $\infty$ to characterise the unique solvability of the Dirichlet problem for degenerate elliptic equations with power-like weights in arbitrary open sets. In the measure-theoretical context, the criterion determines whether the $\A$-harmonic measure of $\infty$ is null or positive. From the topological point of view, it presents a test for the thinness of the exterior set at $\infty$ in the $\A$-fine topology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_15249 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Wiener Criterion at $\infty$ for Degenerate Elliptic Equations Abdulla, Ugur G. Brazke, Denis Analysis of PDEs 35J25, 31C05, 31C15, 31C40 This paper establishes a Wiener criterion at $\infty$ to characterise the unique solvability of the Dirichlet problem for degenerate elliptic equations with power-like weights in arbitrary open sets. In the measure-theoretical context, the criterion determines whether the $\A$-harmonic measure of $\infty$ is null or positive. From the topological point of view, it presents a test for the thinness of the exterior set at $\infty$ in the $\A$-fine topology. |
| title | The Wiener Criterion at $\infty$ for Degenerate Elliptic Equations |
| topic | Analysis of PDEs 35J25, 31C05, 31C15, 31C40 |
| url | https://arxiv.org/abs/2510.15249 |