Homogénéisation du problème de Neumann non homogène dans des ouverts perforés. (Homogeneization of the nonhomogeneous Neumann problem in perforated open domains). (French) Zbl 0683.35026

Summary: We consider the Neumann problem in a domain with periodic holes. The size of the basic cell and of the holes is of order of \(\epsilon\). Some homogeneization theorems are proved. There are essentially two limit cases as \(\epsilon\) \(\to 0\). In the first one the mean value of the data on the boundary of the holes is nonzero. This term gives rise to a nonzero contribution in the right-hand side of the homogenized equation. In the second case, when this mean value is zero, the same homogenized equation as for the homogeneous Neumann problem is obtained. General Fourier conditions are also treated.


35J25 Boundary value problems for second-order elliptic equations