Laplace equation in a domain with a rectilinear crack: higher order derivatives of the energy with respect to the crack length
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.
Mathematics Subject Classification35J20 35C20 74R10
KeywordsCracked domains Energy release rate Higher order derivatives Asymptotic expansion of solutions
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