Numerical calculation of extremal Steklov eigenvalues in 3D and 4D

Antunes, Pedro R. S.

http://hdl.handle.net/10400.2/11814

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Authors

Antunes, Pedro R. S.

Abstract(s)

We develop a numerical method for solving shape optimization of functionals involving Steklov eigenvalues and apply it to the problem of maximization of the k-th Steklov eigenvalue, under volume constraint. A similar study in the planar case was already addressed in the literature using the boundary integral equation method. Here we extend that study to the 3D and 4D cases, using the Method of Fundamental Solutions as the forward solver.