Homogenization of elliptic problems with \(L^p\) boundary data (Q1102444)

The authors consider a homogenization problem, where the coefficients, describing the material property, are periodic and Lipschitz continuous with first derivative. The data on the boundary of the domain is supposed to belong to \(L^p\). If the boundary satisfies a uniform exterior sphere condition, the solution of the boundary problem converges in \(L^p\), when the period goes to zero, to the corresponding homogenized problem. The examples are given showing that this convergence result does not hold for a general \(G\)-convergent sequence of operators and depends on the periodicity of a as well as on its smoothness.