Summary
The asymptotic behaviour of the solutions of a sequence of variational inequalities for the biharmonic operator with variable two-sided obstacles is investigated by describing the form of the limit problem, which is computed explicitly in two meaningful examples.
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References
H. Attouch -C. Picard,Variational inequalities with varying obstacles: the general form of the limit problem, J. Funct. Anal.,50 (1983), pp. 1–44.
D.Cioranescu - L. I.Hedberg - F.Murat,Delta carré et le tapis du fakir, Seminar held by F.Murat at the Scuola Normale Superiore, Pisa (1982).
D. Cioranescu -F. Murat,Un terme étrange venu d'ailleurs, I. Nonlinear partial differential equations and their applications, Collège de France Seminar, vol. III, Res. Notes in Math.,70, Pitman, London (1983), pp. 154–178.
G. Dal Maso,Asymptotic behaviour of minimum problems with bilateral obstacles, Ann. Mat. Pura Appl., (4),129 (1981), pp. 327–366.
G. Dal Maso -L. Modica,Nonlinear stochastic homogenization, Ann. Mat. Pura Appl., (4),144 (1986), pp. 347–389.
G.Dal Maso - G.Paderni,Integral representation of some convex local functionale, Ricerche Mat., to appear.
E. De Giorgi -T. Franzoni,Su un tipo di convergenea variazionale, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur., (8),58 (1975), pp. 842–850.
D. Gilbarg -N. S. Teudinger,Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin, 1983.
E. Ya. Hruslov,The method of orthogonal projections and the Dirichlet problems in domains with a fine-grained boundary, Math. USSR Sb.,17 (1972), pp. 37–59.
E. Ya. Hruslov,The first boundary value problem in domains with a complicated boundary for higher order equations, Math. USSR Sb.,32 (1977), pp. 535–549.
A. V. Marchenko -E. Ya. Hrurlov,Boundary value problems in domains with closed-grained boundary (Russian), Naukova Dumka, Kiev, 1974.
V. G. Maz'ya -V. P. Khavin,Nonlinear potential theory, Russian Math. Surveys,27 (1972), pp. 71–148.
G. Paderni,Limiti di problemi di minimo per funzionali quadratici di ordine superiore con ostacoli, Magister Thesis, S.I.S.S.A., Trieste, 1985.
C.Picard,Problème biharmonique avec obstacles variables, Thèse, Université de Paris-Sud, 1984.
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Dal Maso, G., Paderni, G. Variational inequalities for the biharmonic operator with variable obstacles. Annali di Matematica pura ed applicata 153, 203–227 (1988). https://doi.org/10.1007/BF01762393
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DOI: https://doi.org/10.1007/BF01762393