Shape differentiability of the eigenvalues of elliptic systems
Spectral Theory
2014-11-13 v1 Analysis of PDEs
Abstract
We consider second order elliptic systems of partial differential equations subject to Dirichlet and Neumann boundary conditions. We prove analyticity of the elementary symmetric functions of the eigenvalues, and compute Hadamard-type formulas for such functions. Then we provide a characterization of criticality of the domain under volume constraint, and prove that if the system is rotation invariant, then balls are critical domains for all those functions.
Cite
@article{arxiv.1411.3247,
title = {Shape differentiability of the eigenvalues of elliptic systems},
author = {Davide Buoso},
journal= {arXiv preprint arXiv:1411.3247},
year = {2014}
}
Comments
Submitted for the IMSE 2014 Conference Proceedings