Implicit parametrizations in shape optimization: boundary observation

Cornel Marius Murea, Dan Tiba

Published 2020-03-23Version 1

In the fist section, some results are reviewed. In the second section, we collect some preliminaries on the implicit parametrization theorem, especially in dimension d=2, which is a case of interest in shape optimization. The formulation of the problem is also discussed. The approximation via penalization and its differentiability properties are analyzed in Section 3. Next, we investigate the discretization process in Section 4. The last section is devoted to numerical experiments.