Mathematics

In this talk I will consider the weak solution of the Laplace equation in a planar domain with a straight crack, with a homogeneous Neumann condition on the crack and a nonhomogeneous Dirichlet condition on the rest of the boundary. I will explain how to compute, for every k, 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. I will give the details of the proof in the cases k = 1 and k = 2, and I will sketch the proof for the general case.,/p>

This seminar is part of the AJS series of seminars.