Laplace equation in a domain with a rectilinear crack: higher order derivatives of the energy with respect to the crack length |
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Authors: | Gianni Dal Maso Gianluca Orlando Rodica Toader |
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Institution: | 1.SISSA,Trieste,Italy;2.DIMI,Università di Udine,Udine,Italy |
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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. |
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