Archive for Rational Mechanics and Analysis

, Volume 183, Issue 1, pp 21–58 | Cite as

Some Flows in Shape Optimization

  • Pierre Cardaliaguet
  • Olivier LeyEmail author


Geometric flows related to shape optimization problems of the 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.


Viscosity Solution Interposition Theorem Nonlocal Term Order Partial Differential Equation Shape Optimization Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.UFR des Sciences et TechniquesUniversité de Bretagne OccidentaleBrestFrance
  2. 2.Faculté des Sciences et TechniquesUniversité de Tours, Laboratoire de Mathématiques et Physique ThéoriqueToursFrance

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