Weak shape formulation of free boundary problems

Jean-Paul Zolésio

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1994)

  • Volume: 21, Issue: 1, page 11-44
  • ISSN: 0391-173X

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Zolésio, Jean-Paul. "Weak shape formulation of free boundary problems." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 21.1 (1994): 11-44. <http://eudml.org/doc/84165>.

@article{Zolésio1994,
author = {Zolésio, Jean-Paul},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {free boundary problems; variational inequalities; weak shape formulation; scalar elliptic problems},
language = {eng},
number = {1},
pages = {11-44},
publisher = {Scuola normale superiore},
title = {Weak shape formulation of free boundary problems},
url = {http://eudml.org/doc/84165},
volume = {21},
year = {1994},
}

TY - JOUR
AU - Zolésio, Jean-Paul
TI - Weak shape formulation of free boundary problems
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1994
PB - Scuola normale superiore
VL - 21
IS - 1
SP - 11
EP - 44
LA - eng
KW - free boundary problems; variational inequalities; weak shape formulation; scalar elliptic problems
UR - http://eudml.org/doc/84165
ER -

References

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  1. [1] H.W. Alt - L.A. Caffarelli, Existence and Regularity for a Minimum Problem with Free Boundary. Preprint of Courant Institute, N.Y, 1980. Zbl0449.35105MR618549
  2. [2] E. De Giorgi - F. Colombini L.C. Piccinini, Frontiere orientate di misura minima e questioni collegate. Scuola Normale Superiore, Pisa, 1972. Zbl0296.49031MR493669
  3. [3] M.C. Delfour - J.P. Zolésio, Velocity Method and Lagrangian Formulation for the Computation of the Shape Hessian. SIAM J. Control Optim.29 (1991), 1414-1442. Zbl0747.49007MR1132189
  4. [4] J. Deny - J.L. Lions, Les espaces du type de Beppo Levi. Ann. Inst. Fourier (Grenoble) 5 (1953), 305-370. Zbl0065.09903MR74787
  5. [5] A. Fasano, Lecture at the Nato Advance Study Shape Optimization and Free Boundary Problems, Montréal, 1990. 
  6. [6] H. Federer - W.P. Ziemer, The Lebesgue Set of a Function Whose Distribution Derivative are p-th Power Summable. Indiana Univ. Math. J.22 (1972), 139-158. Zbl0238.28015MR435361
  7. [7] J. Sokolowski - J.P. Zolésio, Introduction to Shape Optimization. Shape Sensitivity Analysis. Computational Mathematics, vol. 16, Springer-Verlag, 1992. Zbl0761.73003MR1215733
  8. [8] G. Stampacchia, Seminaire de mathématiques supérieures. Presse de l'Université de Montréal, 1960. 
  9. [9] R. Témam, Problèmes mathématiques en plasticité. Gauthier-Villars, Paris, 1983. Zbl0547.73026MR711964
  10. [10] J.P. Zolésio, Un résultat d'existence de vitesse convergente en optimisation de domaine. C.R. Acad. Sci. Paris Sér. I Math.283 (1976), 855-859. Zbl0343.49004MR428158
  11. [11] J.P. Zolésio, Optimisation de domaine par déformation. Thèse de Doctorat d'état. Nice (France), 1979. 
  12. [12] J.P. Zolésio, Problème á frontiere libre issu de la physique des plasmas. C.R. Acad. Sci. Paris Sér. I Math, 188 (1979), 910-914. 
  13. [13] J.P. Zolésio, The Material Derivative (or Speed Method) for Shape Optimization. In Optimization of Distributed Parameter Systems, J. Céa, E. Haug eds., Sijthoff aand Noordhoff, 1980, 1089-1154. Zbl0517.73097MR690991
  14. [14] J.P. Zolésio, Shape Variational Formulation for Free Boundary Value Problems. In Optimization of Distributed Parameter Systems, J. Céa, E. Haug eds., Sijthoff aand Noordhoff, 1980, 1155-1194. 
  15. [15] J.P. Zolésio, Numerical Algorithms and Existence Result for a Bernoulli-like Steady Free Boundary Problem. Large Scale System, Elsevier Publ. (North-Holland) 6 (1984) 263-278. Zbl0552.49027MR780683
  16. [16] J.P. Zolésio, Shape Derivative and Shape Acceleration in Boundary Value Problems. Lecture notes in Control and Information Sc., 104 (1988), 153-191, A. Bermudez ed., Springer-Verlag, Heidelberg-Berlin-New York- Tokyo, 1988. MR987990

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