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arXiv · 2505.01534

Fredholm properties of singular elliptic operators arising in the study of point defects

Gabriela Jaramillo
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Abstract

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.

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Gabriela Jaramillo. 2025-05-02. Fredholm properties of singular elliptic operators arising in the study of point defects. https://arxiv.org/abs/2505.01534

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