A p-Laplacian approximation for some mass optimization problems

Journal of Optimization Theory and Applications

Volumn 118, Issue 1, 2003, Pages 1-25

  Bouchitte G ^a   Buttazzo, G ^b   De Pascale, L ^b  

^a UNIVERSITÉ DE TOULON   (France)

^b UNIVERSITY OF PISA   (Italy)

Author keywords

Mass transportation problems; Monge Kantorovich differential equation; p Laplacian; Shape optimization

Indexed keywords

DIFFERENTIAL EQUATIONS; LAPLACE TRANSFORMS; SHAPE OPTIMIZATION;

LAPLACIAN APPROXIMATIONS; MASS DISTRIBUTION; MASS OPTIMIZATION; MASS TRANSPORTATION PROBLEM; MONGE-KANTOROVICH DIFFERENTIAL EQUATION; OPTIMIZATION PROBLEMS; P-LAPLACE EQUATION; P-LAPLACIAN; SHAPE-OPTIMIZATION; TRANSPORTATION PROBLEM;

MASS TRANSPORTATION;

EID: 0037492025     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1024751022715     Document Type: Article

References (14)

1. BOUCHITTÉ, G., and BUTTAZZO, G., Characterization of Optimal Shapes and Masses through the Monge-Kantorovich Equation, Journal of the European Mathematical Society, Vol. 3, pp. 139-168, 2001.
2. BOUCHITTÉ, G., BUTTAZZO, G., and SEPPECHER, P., Energy with Respect to a Measure and Applications to Low-Dimensional Structures, Calculus of Variations and Partial Differential Equations, Vol. 5, pp. 37-54, 1997.
3. EVANS, L. C., and GANGBO, W., Differential Equations Methods for the Monge-Kantorovich Mass Transfer Problem, Memoires of the American Mathematical Society, Providence, Rhode Island, Vol. 137, 1999.
4. EVANS, L. C., Partial Differential Equations and Monge-Kantorovich Mass Transfer, Current Developments in Mathematics 1997, International Press, Boston, Massachusetts, pp. 65-126, 1999.
5. FELDMAN, M., and MCCANN, R. J., Monge's Transport Problem on a Riemannian Manifold, Transactions of the American Mathematical Society, Vol. 354, pp. 1667-1697, 2002.
6. AMBROSIO, L., Lecture Notes on Optimal Transport Problems, Lectures given in Madeira, Portugal, 2-9 July 2000. Preprint available on http://cvgmt.sns.it/ people/ambrosio/.
7. GOLAY, F., and SEPPECHER, P., Locking Materials and the Topology of Optimal Shapes, European Journal of Mechanics/Solids, Vol. 20A, pp. 631-644, 2001.
8. BOUCHITTÉ, G., BUTTAZZO, G., and SEPPECHER, P., Shape Optimization Solutions via Monge-Kantorovich Equation, Comptes Rendus de l' Academie de Sciences de Paris, Vol. 324, pp. 1185-1191, 1997.
9. DEMENGEL, F., Déplacements á Déformations Bornées et Champs de Contrainte Mesures, Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, Vol. 12, pp. 243-318, 1985.
10. BOUCHITTÉ, G., BUTTAZZO, G., and FRAGALÁ, I., Mean Curvature of a Measure and Related Variational Problems, Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, Vol. 25, pp. 179-196, 1997.
11. BOUCHITTÉ, G., BUTTAZZO, G., and FRAGALÁ, I., Convergence of Sobolev Spaces on Varying Manifolds, Journal of Geometric Analysis, Vol. 11, pp. 399-422, 2001.
12. FRAGALÁ, I., and MANTEGAZZA, C., On Some Notion of Tangent Space to a Measure, Proceedings of the Royal Society of Edinburgh, Mathematics, Vol. 129A, pp. 331-342, 1999.
13. HUTCHINSON, J. E., Second Fundamental Form for Varifolds and the Existence of Surfaces Minimizing Curvature, Indiana University Mathematics Journal, Vol. 35, pp. 45-71, 1986.
14. ALLAIRE, G., and KOHN, R. V., Optimal Design for Minimum Weight and Compliance in Plane Stress Using Extremal Microstructures, European Journal of Mechanics/Solids, Vol. 12A, pp. 839-878, 1993.