Regularity of optimal shapes for the Dirichlet's energy with volume constraint

ESAIM - Control, Optimisation and Calculus of Variations

Volumn 10, Issue 1, 2004, Pages 99-122

  Briancon, Tanguy ^a,b  

^a UNIVERSITÉ DE RENNES 1   (France)

^b UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

Calculus of variations; Free boundary; Geometrical measure theory; Shape optimization

Indexed keywords

DIRICHLET ENERGY; EULER-LAGRANGE EQUATION; OPTIMAL SHAPES; REGULARITY; VOLUME CONSTRAINTS;

BOUNDARY CONDITIONS; CONSTRAINT THEORY; FUNCTIONS; MATHEMATICAL TECHNIQUES; THEOREM PROVING; VOLUME MEASUREMENT;

SET THEORY;

EID: 12844268099     PISSN: 12928119     EISSN: 12623377     Source Type: Journal    
DOI: 10.1051/cocv:2003038     Document Type: Article

References (15)

1. N. Aguilera, H.W. Alt and L.A. Caffarelli, An optimization problem with volume constraint. SIAM J. Control Optimization 24 (1986) 191-198.
2. H.W. Alt and L.A. Caffarelli, Existence and regularity for a minimum problem with free boundary. J. Reine Angew. Math. 325 (1981) 105-144.
3. H.W. Alt, L.A. Caffarelli and A. Friedman, Variational problems with two phases and their free boundaries. Trans. Am. Math. Soc. 282 (1984) 431-461.
4. T. Briancon, Problèmes de régularité en optimisation de formes. Ph.D. thesis, universite Rennes 1 (2002).
5. M. Crouzeix, Variational approach of a magnetic shaping problem. Eur. J. Mech. 10 (1991) 527-536.
6. L.C. Evans and R.F. Gariepy, Measure theory and fine properties of functions. CRC Press (1992).
7. H. Federer, Geometric measure theory. Springer-Verlag (1969).
8. D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order. Springer-Verlag (1983).
9. E. Giusti, Minimal surfaces and functions of bounded variation. Birkhauser (1986).
10. B. Gustafsson and H. Shahgholian, Existence and geometric properties of solutions of a free boundary problem in potential theory. J. Reine Angew. Math. 473 (1996) 137-179.
11. M. Hayouni, Existence et régularité pour des problèmes d’optimisation de formes. Ph.D. thesis, universite Henri Poincare Nancy 1 (1997).
12. M. Hayouni, Lipschitz continuity of the state function in a shape optimization problem. J. Convex Anal. 6 (1999) 71-90.
13. M. Hayouni, T. Briancon and M. Pierre. On a volume constrained shape optimization problem with nonlinear state equation. (to appear).
14. X. Pelgrin, Etude d’un problème ' frontière libre bidimensionnel. Ph.D. thesis, universite Rennes 1 (1994).
15. T.H. Wolff, Plane harmonic measures live on sets of a-finite length. Ark. Mat. 31 (1993) 137-172.