Square integrable surface potentials on non-smooth domains and application to the Laplace equation in $L^2$ - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

Square integrable surface potentials on non-smooth domains and application to the Laplace equation in $L^2$

Résumé

Motivated by applications in fluid dynamics involving the harmonic Bergman projection we aim at extending the theory of single and double layer potentials (well documented for functions with $H^1_{\ell oc}$ regularity) to locally square integrable functions. Having in mind numerical simulations in 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).
Fichier principal
Vignette du fichier
weak_single_layer_6.pdf (459.63 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03942972 , version 1 (17-01-2023)
hal-03942972 , version 2 (25-05-2023)

Identifiants

Citer

Alexandre Munnier. Square integrable surface potentials on non-smooth domains and application to the Laplace equation in $L^2$. 2023. ⟨hal-03942972v2⟩
44 Consultations
33 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More