Lorena Bociu
North Carolina State University

Shape Calculus for Wave Equations with Neumann Boundary Conditions

Shape differentiability is a fundamental question in shape optimization and control problems. The shape derivative analysis has been considered and resolved for many classical linear problems. However, the situation is more delicate for wave equations with Neumann boundary conditions, due to the lack of good boundary regularity for the solution, which is a key ingredient in the differentiability analysis. We provide a full analysis of shape differentiability for the solution to the second order hyperbolic equation with Neumann boundary conditions and also discuss a hidden boundary regularity result, which we obtained through a new pseudo-extractor technique.
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