Homogenization of some singular nonlinear elliptic problems

The paper deals with the asymptotic behaviour of the solutions of quasilinear elliptic Dirichlet problems when the (linear) principal parts H-converge and the lower order terms exhibit a natural growth in the gradient variable and a singular behaviour in the u variable. The lower order term in the limit problem presents the same singularity in the u variable and the same growth in the gradient variable. The quadratic nonlinearity in the gradient is constructed through the correctors associated to the principal parts, on which natural integrability hypotheses are assumed. © 2011 Academic Publications, Ltd.