Square‐Integrable Surface Potentials on Nonsmooth Domains and Application to the Laplace Equation in L<sup>2</sup>
ABSTRACT Motivated by applications in fluid dynamics involving the harmonic Bergman projection, we aim to extend the theory of single and double layer potentials (well documented for functions with regularity) to locally square integrable functions. Having in mind numerical simulations for which functions are usually defined on a polygonal mesh, we wish this theory to cover the cases of non‐smooth domains (i.e., with Lipschitz continuous or polygonal boundaries).
Authors
- Alexandre Munnier
Institutions
- Centre National de la Recherche Scientifique (FR)
- Institut Élie Cartan de Lorraine (FR)
- Université de Lorraine (FR)
Publication Details
- Journal
- Mathematical Methods in the Applied Sciences
- Published
- 2025-03-29
- DOI
- https://doi.org/10.1002/mma.10837
- Primary Topic
- Numerical methods in inverse problems
- Type
- article
- Field-Weighted Citation Impact
- 0.00