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

TitleLaplace equation in a domain with a rectilinear crack: higher order derivatives of the energy with respect to the crack length
Publication TypeJournal Article
Year of Publication2014
AuthorsDal Maso, G, Orlando, G, Toader, R
Keywordscracked domains, energy release rate, higher order derivatives, asymptotic expansion of solutions
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.

URLhttp://hdl.handle.net/1963/7271
DOI10.1007/s00030-014-0291-0

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