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Square integrable surface potentials on non-smooth domains and application to the Laplace equation in L2
  • Alexandre Munnier
Alexandre Munnier
Institut Elie Cartan de Lorraine

Corresponding Author:[email protected]

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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 H ℓoc 1 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).
08 Jul 2023Submitted to Mathematical Methods in the Applied Sciences
08 Jul 2023Assigned to Editor
08 Jul 2023Submission Checks Completed
14 Jul 2023Review(s) Completed, Editorial Evaluation Pending
22 Jul 2023Reviewer(s) Assigned