Tartar's method of compensated compactness in averaging the spectrum of a mixed problem for an elliptic equation in a perforated domain with third boundary condition
Svetlana Evgenievna Pastukhova · Sbornik Mathematics · 1995
We study the?problem described in the?title of this paper in the?domain obtained from a?domain by periodic perforation with period , where is the?unit cube in . For this problem we use the?method of compensated compactness to obtain the?first two terms of the?asymptotics of the?-th eigenvalue in powers of as : , where is a?constant independent of and is the?-th eigenvalue of the?averaged problem (which turns out to be the?Dirichlet problem in the?domain ) for .