Homogenization of some variational inequalities with restrictions on subsets ɛ-periodically located along the domain boundary
M. N. Zubova, Т. А. Шапошникова · Moscow University Mathematics Bulletin · 2007
In this paper some problems concerning homogenization of variational inequalities for the Laplace operator and the biharmonic operator with restrictions on subsets ɛ-periodically located along the domain boundary are studied (ɛ is a small parameter). These subsets are collections of balls of radius a ɛ a. An asymptotics of solutions is obtained in the so-called critical case characterized by a specific relation between the period ɛ and the value a ɛ. Strong convergence of solutions and their gradients is also established.