We consider the weak solution of the Laplace equation in a planar domain with a straight crack, prescribing a homogeneous Neumann condition on the crack and a nonhomogeneous Dirichlet condition on the rest of the boundary. For every k we express the k-th derivative of the energy with respect to the crack length in terms of a finite number of coefficients of the asymptotic expansion of the solution near the crack tip and of a finite number of other parameters, which only depend on the shape of the domain.

Laplace equation in a domain with a rectilinear crack: higher order derivatives of the energy with respect to the crack length / Dal Maso, Gianni; Orlando, Gianluca; Toader, Rodica. - In: NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS. - ISSN 1021-9722. - 22:3(2015), pp. 449-476. [10.1007/s00030-014-0291-0]

Laplace equation in a domain with a rectilinear crack: higher order derivatives of the energy with respect to the crack length

Dal Maso, Gianni
;
Orlando, Gianluca;Toader, Rodica
2015-01-01

Abstract

We consider the weak solution of the Laplace equation in a planar domain with a straight crack, prescribing a homogeneous Neumann condition on the crack and a nonhomogeneous Dirichlet condition on the rest of the boundary. For every k we express the k-th derivative of the energy with respect to the crack length in terms of a finite number of coefficients of the asymptotic expansion of the solution near the crack tip and of a finite number of other parameters, which only depend on the shape of the domain.
2015
22
3
449
476
http://preprints.sissa.it/xmlui/handle/1963/7271
Dal Maso, Gianni; Orlando, Gianluca; Toader, Rodica
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/14396
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