Fredholm properties of singular elliptic operators arising in the study of point defects
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916717888798720 |
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| author | Jaramillo, Gabriela |
| author_facet | Jaramillo, Gabriela |
| contents | Motivated by the dynamics of defects in planar pattern-forming systems, we study Fredholm properties of elliptic operators with singular coefficients in weighted Sobolev spaces. In particular, we consider a family of doubly weighted spaces that encode algebraic decay/growth of functions at infinity, and near the origin. Our results give conditions on the weights under which the operators are either injective, surjective, or isomorphisms. We also give a precise description of the kernel and range of these operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_01534 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fredholm properties of singular elliptic operators arising in the study of point defects Jaramillo, Gabriela Analysis of PDEs Functional Analysis 46N20, 35J10 Motivated by the dynamics of defects in planar pattern-forming systems, we study Fredholm properties of elliptic operators with singular coefficients in weighted Sobolev spaces. In particular, we consider a family of doubly weighted spaces that encode algebraic decay/growth of functions at infinity, and near the origin. Our results give conditions on the weights under which the operators are either injective, surjective, or isomorphisms. We also give a precise description of the kernel and range of these operators. |
| title | Fredholm properties of singular elliptic operators arising in the study of point defects |
| topic | Analysis of PDEs Functional Analysis 46N20, 35J10 |
| url | https://arxiv.org/abs/2505.01534 |