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Regularity of solutions of elliptic problems with a curved fracture

Abstract : 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
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Contributor : Frédéric Pruvost Connect in order to contact the contributor
Submitted on : Tuesday, February 23, 2021 - 1:35:43 PM
Last modification on : Wednesday, July 6, 2022 - 3:08:54 PM

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



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