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Codegone, Marco; Rodrigues, Jose-Francisco

Convergence of the coincidence set in the homogenization of the obstacle problem. (English) Zbl 0493.49008

Ann. Fac. Sci. Toulouse, V. Ser., Math. 3, 275-285 (1981).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
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Cited in 3 Documents

MSC:

49J40 Variational inequalities
49J45 Methods involving semicontinuity and convergence; relaxation
35B40 Asymptotic behavior of solutions to PDEs
35B65 Smoothness and regularity of solutions to PDEs
35R35 Free boundary problems for PDEs

Keywords:

obstacle problem; homogenization; Hausdorff metric; coincidence set
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References:

[1] 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. · Zbl 0404.49007
[2] Beer, G.A.«Hausdorff Metric and Convergence in Measure». Michigan Math. J.21, (1974), 63-64. · Zbl 0287.28012
[3] Bensoussan, A. & Lions, J.L. & Papanicolaou, G.. «Asymptotic Analysis for Periodic Structures». North Holland, Amsterdam (1978). · Zbl 0404.35001
[4] Biroli, M.«G-Convergence for elliptic variational and quasivariational inequalities». pp. 361-383 in « Recent Methods...» see [A]. · Zbl 0406.49003
[5] Biroli, M.«A De Giorgi-Nash-Moser result for a variational ineguality». Boll. U.M.I., 16 - A, (1979), 598-605. · Zbl 0424.35035
[6] Boccardo, L. & Capuzzo Dolcetta, I.. «G-Convergenza et problema di Dirichlet unilateral». Bol. U.M.I. (4) 12, (1975), 115-123. · Zbl 0337.35023
[7] Boccardo, L. & Marcellini, P.. «Sulla convergenza della soluzioni di disequazioni variazionali». Annali Mat. Pura Appl. (IV)110, (1976), 137-159. · Zbl 0333.35030
[8] Boccardo, L. & Murat, F.. «Homogénéisation et convergence au sens de Mosco de convexes unilatéraux». (to appear).
[9] Caffarelli, L.A.«The regularity of Free Boundaries in Higher Dimensions». Acta Math.139, (1977),155-184. · Zbl 0386.35046
[10] Codegone, M. & Rodrigues, J.F.. «On the Homogenization of the Rectangular Dam Problem». Rend. Sem. Mat. Torino Vol. 39°, 2 (1981). · Zbl 0514.35030
[11] De Giorgi, E. & Spagnolo, S.. «Sulla convergenza degli integrali dell’energia per operatori ellittici del 2o ordine». Boll. U.M.I. (4), 8 (1973), 391-411. · Zbl 0274.35002
[12] De Giorgi, E.«Convergence Problems for Functionals and Operators». pp. 131-188, in «Recent Methods...» see [A]. · Zbl 0405.49001
[13] Dellacherie, C.«Ensembles Analytiques. Capacités. Mesures de Hausdorff». no 295, Springer-Verlag, Berlin (1972). · Zbl 0259.31001
[14] Lewy, H. & Stampacchia, G.. «On the regularity of the solution of a variational inequality)). Comm. Pure Appl. Math.22, (1969), 153-188. · Zbl 0167.11501
[15] 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] Murat, F.Oral communication. Paris (1980).
[17] Murthy, M.K.V. & Stampacchia, G.. «A variational inequality with mixed boundary conditions». Israel J. Math.13, (1972), 188-223. · Zbl 0255.35027
[18] Pironneau, O. & Saguez, C.. «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] Rodrigues, J.F.«Sur le comportement asymptotique de la solution et de la frontière libre d’une inéquation variationnelle parabolique». Ann. Fac. Sc. Toulouse.
[20] Rodrigues, J.F.«Free Boundary Convergence in the Homogenization of the One Phase Stefan Problem». Trans. Ameri. Math. Soc. · Zbl 0504.35079
[21] Tartar, L.Cours Peccot, Collège de France. Paris (1977), see also Murat, F.«H-convergence». Conférences Univ. Alger (1978).
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