Convergence of the coincidence set in the homogenization of the obstacle problem

Marco Codegone; José-Francisco Rodrigues

Annales de la Faculté des sciences de Toulouse : Mathématiques (1981)

  • Volume: 3, Issue: 3-4, page 275-285
  • ISSN: 0240-2963

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Codegone, Marco, and Rodrigues, José-Francisco. "Convergence of the coincidence set in the homogenization of the obstacle problem." Annales de la Faculté des sciences de Toulouse : Mathématiques 3.3-4 (1981): 275-285. <http://eudml.org/doc/73125>.

@article{Codegone1981,
author = {Codegone, Marco, Rodrigues, José-Francisco},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {obstacle problem; homogenization; Hausdorff metric; coincidence set},
language = {eng},
number = {3-4},
pages = {275-285},
publisher = {UNIVERSITE PAUL SABATIER},
title = {Convergence of the coincidence set in the homogenization of the obstacle problem},
url = {http://eudml.org/doc/73125},
volume = {3},
year = {1981},
}

TY - JOUR
AU - Codegone, Marco
AU - Rodrigues, José-Francisco
TI - Convergence of the coincidence set in the homogenization of the obstacle problem
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 1981
PB - UNIVERSITE PAUL SABATIER
VL - 3
IS - 3-4
SP - 275
EP - 285
LA - eng
KW - obstacle problem; homogenization; Hausdorff metric; coincidence set
UR - http://eudml.org/doc/73125
ER -

References

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  1. [A] Attouch A.«Convergence des solutions d'inéquations variationnelles avec obstacle». In Proc. Int. Meet. on Recent Methods in Non Linear Analysis (Rome 1978) Edited by E. De Giorgi, E. Magenes and U. Mosco. Pitagora Ed., Bologna (1979) pp. 101-113. Zbl0404.49007MR533164
  2. [B] Beer G.A.«Hausdorff Metric and Convergence in Measure». Michigan Math. J.21, (1974), 63-64. Zbl0287.28012MR367161
  3. [BLP] Bensoussan A. & J.L. Lions & G. Papanicolaou. «Asymptotic Analysis for Periodic Structures». North Holland, Amsterdam (1978). Zbl0404.35001
  4. [Bi1] Biroli M.«G-Convergence for elliptic variational and quasivariational inequalities». pp. 361-383 in « Recent Methods...» see [A]. Zbl0406.49003MR533176
  5. [Bi2] Biroli M.«A De Giorgi-Nash-Moser result for a variational ineguality». Boll. U.M.I., 16 - A, (1979), 598-605. Zbl0424.35035MR551388
  6. [BC] Boccardo L. & I. Capuzzo Dolcetta. «G-Convergenza et problema di Dirichlet unilateral». Bol. U.M.I. (4) 12, (1975), 115-123. Zbl0337.35023
  7. [BMa] Boccardo L. & P. Marcellini. «Sulla convergenza della soluzioni di disequazioni variazionali». Annali Mat. Pura Appl. (IV)110, (1976), 137-159. Zbl0333.35030
  8. [BMu] Boccardo L. & F. Murat. «Homogénéisation et convergence au sens de Mosco de convexes unilatéraux». (to appear). 
  9. [C] Caffarelli L.A.«The regularity of Free Boundaries in Higher Dimensions». Acta Math.139, (1977),155-184. Zbl0386.35046MR454350
  10. [CR] Codegone M. & J.F. Rodrigues. «On the Homogenization of the Rectangular Dam Problem». Rend. Sem. Mat. Torino Vol. 39°, 2 (1981). Zbl0514.35030
  11. [DS] De Giorgi E. & S. Spagnolo. «Sulla convergenza degli integrali dell'energia per operatori ellittici del 2o ordine». Boll. U.M.I. (4), 8 (1973), 391-411. Zbl0274.35002
  12. [DG] De Giorgi E.«Convergence Problems for Functionals and Operators». pp. 131-188, in «Recent Methods...» see [A]. Zbl0405.49001MR533166
  13. [De] Dellacherie C.«Ensembles Analytiques. Capacités. Mesures de Hausdorff». Lect. Notes in Math. no 295, Springer-Verlag, Berlin (1972). Zbl0259.31001MR492152
  14. [LS] Lewy H. & G. Stampacchia. «On the regularity of the solution of a variational inequality)). Comm. Pure Appl. Math.22, (1969), 153-188. Zbl0167.11501
  15. [M1] Murat F.«Sur l'homogénéisation d'inéquations elliptiques du 2ème ordre relative au convexe K(ψ1,ψ2)». Thèse d'Etat, Univ. Paris VI (1976). 
  16. [M2] Murat F.Oral communication. Paris (1980). 
  17. [MS] Murthy M.K.V. & G. Stampacchia. «A variational inequality with mixed boundary conditions». Israel J. Math.13, (1972), 188-223. Zbl0255.35027
  18. [PS] Pironneau O. & C. Saguez. «Asymptotic behaviour with respect to the domain of solutions of Partial Differential Equations». Rapport no 218, I.R.I.A. Laboria, Rocquencourt, France (1977). 
  19. [R1] Rodrigues J.F.«Sur le comportement asymptotique de la solution et de la frontière libre d'une inéquation variationnelle parabolique». Ann. Fac. Sc. Toulouse. MR701732
  20. [R2] Rodrigues J.F.«Free Boundary Convergence in the Homogenization of the One Phase Stefan Problem». Trans. Ameri. Math. Soc. Zbl0504.35079MR670933
  21. [T] Tartar L.Cours Peccot, Collège de France. Paris (1977), see also F. Murat«H-convergence». Conférences Univ. Alger (1978). 

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