Homogenization of a nonlinear elliptic problem with large nonlinear potential

Abstract

Homogenization is studied for a nonlinear elliptic boundary-value problem with a large nonlinear potential. More specifically we are interested in the asymptotic behaviour of a sequence of p-Laplacians of the form

It is shown that, under a centring condition on the potential V, there exists a two-scale homogenized system with solution (u, u ₁) such that the sequence u _ϵ of solutions converges weakly to u in W ^1,p and the gradients D _x u _ϵ two-scale converges weakly to D _x u + D _y u ₁ in L ^p , respectively. We characterize the limit system explicitly by means of two-scale convergence and a new convergence result.

Keywords:

• nonlinear
• potential
• homogenization

AMS Subject Classifications:

• 35B27
• 35B40