Abstract
We study the asymptotic behavior of the solution of a boundary value problem for the p-Laplace operator with rapidly alternating nonlinear boundary conditions posed on e-periodically arranged subsets on the boundary of a domain Ω ⊂ ℝn. We assume that p = n, construct a homogenized problem, and prove the weak convergence as e → 0 of the solution of the original problem to the solution of the homogenized problem in the so-called critical case, which is characterized by the fact that the homogenization changes the character of nonlinearity of the boundary condition.
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