Journal article
Hadamard’s Formula Inside and Out
Journal of optimization theory and applications, v 146(3), pp 654-690
2010
Abstract
Our goal is to explore boundary variations of spectral problems from the calculus of moving surfaces point of view. Hadamard’s famous formula for simple Laplace eigenvalues under Dirichlet boundary conditions is generalized in a number of significant ways, including Neumann and mixed boundary conditions, multiple eigenvalues, and second order variations. Some of these formulas appear for the first time here. Furthermore, we present an analytical framework for deriving general formulas of the Hadamard type.
The presented analysis finds direct applications in shape optimization and other variational problems. As a specific application, we discuss equilibrium and stable shapes of electron bubbles.
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Details
- Title
- Hadamard’s Formula Inside and Out
- Creators
- P. Grinfeld - Drexel University
- Publication Details
- Journal of optimization theory and applications, v 146(3), pp 654-690
- Publisher
- Springer US
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000282708600007
- Scopus ID
- 2-s2.0-77956467207
- Other Identifier
- 991019312457904721
InCites Highlights
Data related to this publication, from InCites Benchmarking & Analytics tool:
- Web of Science research areas
- Mathematics, Applied
- Operations Research & Management Science