Reinforcement problems for elliptic equations and variational inequalities

Abstract

Consider the Dirichlet problem for an elliptic equation in a domain Ω, with coefficients having discontinuity on a surface Γ. Suppose Γ divides Ω into Ω1∪ Ω2(Ω2 the inner core), the thickness of Ω1 is of order of magnitude e{open}, and the modulus of ellipticity in Ω1 is of order magnitude λ1. The asymptotic behavior of the solution is studied as e{open} → 0, λ1 → 0, provided lim (e{open}/λ1) exists. Other questions of this type are studied both for elliptic equations and for elliptic variational inequalities. © 1980 Fondazione Annali di Matematica Pura ed Applicata.