Homogenization of variational inequalities for a biharmonic operator with constraints on subsets ε-periodically placed along a manifold of large dimension
Tóm tắt
Behavior of solutions of variational inequalities for a biharmonic operator is studied. These inequalities correspond to one-sided constraints on subsets of a domain Ω placed ε-periodically. All possible behavior types of solutions u
ε
of variational inequalities are considered for ε → 0 depending on relations between small parameters, which are the structure period ε and the contraction coefficient a
ε
of subsets where one-sided constraints are posed.
Tài liệu tham khảo
C. Picard, Problème Biharmonique avec Obstacles Variables, Thèse (Universitè Paris-Sud, 1984).
G. Dal Maso and G. Paderni, “Variational Inequalities for the Biharmonic Operator with Variable Obstacles,” Ann. Mat. pura ed appl., No. 4, 327.
M. N. Zubova, “Homogenization of Variational Inequalities for the Biharmonic Operator with Constraints on ε-Periodically Arranged Subsets,” Differ. Uravn. 42, 801 (2006) [Diff. Equations 42, 853 (2006)]
I. Ekeland and R. Temam, Convex Analysis and Variational Problems (North-Holland, 1972; Mir, Moscow, 1979).
T. A. Shaposhnikova, “On the Averaging of the Dirichlet Problem for a Multiharmonic Equation in Regions Perforated along a Manifold with Large Codimension,” Moscow Math. Soc. 61, 139 (2000).
S. L. Sobolev, Some Applications of Functional Analysis in Mathematical Physics (Nauka, Moscow, 1988) [in Russian].
O. A. Ladyzhenskaya and N. N. Uraltseva, Linear and Quasilinear Elliptic Equations (Nauka, Moscow, 1964; Academic Press, New York, 1968).
D. Kinderlerer and G. Stampacchia, An Introduction to Variational Inequalities and Their Applications (Academic Press, New York, 1980; Mir, Moscow, 1983).