Some flows in shape optimization
Analysis of PDEs
2010-02-15 v1
Abstract
Geometric flows related to shape optimization problems of Bernoulli type are investigated. The evolution law is the sum of a curvature term and a nonlocal term of Hele-Shaw type. We introduce generalized set solutions, the definition of which is widely inspired by viscosity solutions. The main result is an inclusion preservation principle for generalized solutions. As a consequence, we obtain existence, uniqueness and stability of solutions. Asymptotic behavior for the flow is discussed: we prove that the solutions converge to a generalized Bernoulli exterior free boundary problem.
Cite
@article{arxiv.1002.2501,
title = {Some flows in shape optimization},
author = {Pierre Cardaliaguet and Olivier Ley},
journal= {arXiv preprint arXiv:1002.2501},
year = {2010}
}