Using Self-adjoint Extensions in Shape Optimization
نویسندگان
چکیده
Self-adjoint extensions of elliptic operators are used to model the solution of a partial differential equation defined in a singularly perturbed domain. The asymptotic expansion of the solution of a Laplacian with respect to a small parameter ε is first performed in a domain perturbed by the creation of a small hole. The resulting singular perturbation is approximated by choosing an appropriate selfadjoint extension of the Laplacian, according to the previous asymptotic analysis. The sensitivity with respect to the position of the center of the small hole is then studied for a class of functionals depending on the domain. A numerical application for solving an inverse problem is presented. Error estimates are provided and a link to the notion of topological derivative is established.
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