Regularity of solutions of elliptic problems with a curved fracture - Université Polytechnique des Hauts-de-France Accéder directement au contenu
Article Dans Une Revue Journal of Mathematical Analysis and Applications Année : 2017

Regularity of solutions of elliptic problems with a curved fracture

Résumé

We consider the Laplace equation with a right-hand side concentrated on a curved fracture of class Cm+2 for some nonnegative integer m (i.e., a sort of Dirac mass). We show that the solution belongs to a weighted Sobolev space of order m, the weight being the distance to this fracture. Our proof relies on a priori estimates in a dihedron or a cone with singularities for elliptic operators with variable coefficients. In both cases, such an estimate is obtained using a dyadic covering of the domain

Dates et versions

hal-03149894 , version 1 (23-02-2021)

Identifiants

Citer

S. Ariche, Colette De Coster, Serge Nicaise. Regularity of solutions of elliptic problems with a curved fracture. Journal of Mathematical Analysis and Applications, 2017, 447 (2), pp.908-932. ⟨10.1016/j.jmaa.2016.10.021⟩. ⟨hal-03149894⟩
20 Consultations
1 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More