On the energy of a flow arising in shape optimization
Analysis of PDEs
2009-02-13 v1 Optimization and Control
Abstract
In Cardaliaguet-Ley (2006) we have defined a viscosity solution for the gradient flow of the exterior Bernoulli free boundary problem. We prove here that the associated energy is non decreasing along the flow. This justifies the "gradient flow" approach for such kind of problem. The proof relies on the construction of a discrete gradient flow in the flavour of Almgren-Taylor-Wang (1993) and on proving it converges to the viscosity solution.
Keywords
Cite
@article{arxiv.math/0607255,
title = {On the energy of a flow arising in shape optimization},
author = {Pierre Cardaliaguet and Olivier Ley},
journal= {arXiv preprint arXiv:math/0607255},
year = {2009}
}