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

Article

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.

Mathematics Subject Classification

35J20 35C20 74R10 

Keywords

Cracked domains Energy release rate Higher order derivatives Asymptotic expansion of solutions 

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Copyright information

© Springer Basel 2014

Authors and Affiliations

  • Gianni Dal Maso
    • 1
  • Gianluca Orlando
    • 1
  • Rodica Toader
    • 2
  1. 1.SISSATriesteItaly
  2. 2.DIMIUniversità di UdineUdineItaly

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