arXiv Analytics

Sign in

arXiv:math/0607255 [math.AP]AbstractReferencesReviewsResources

On the energy of a flow arising in shape optimization

Pierre Cardaliaguet, Olivier Ley

Published 2006-07-11Version 1

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.

Journal: Interfaces Free Bound. 10, 2 (2008) 223-243
Categories: math.AP, math.OC
Related articles: Most relevant | Search more
arXiv:1303.3219 [math.AP] (Published 2013-03-13, updated 2013-10-31)
Viscosity solution of Hamilton-Jacobi equation by a limiting minmax method
arXiv:1905.00168 [math.AP] (Published 2019-05-01)
On viscosity solutions of space-fractional diffusion equations of Caputo type
arXiv:1809.05317 [math.AP] (Published 2018-09-14)
Uniqueness of the viscosity solution of a constrained Hamilton-Jacobi equation

Links

Toolbox