Homogenization of a nonlinear elliptic problem with large nonlinear potential
Artikel i vetenskaplig tidskrift, 2012

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 -div(a(x/epsilon)vertical bar Du(epsilon vertical bar)(p-2)Du(epsilon)) + 1/epsilon V(x/epsilon)vertical bar u(epsilon)vertical bar(p-2)u(epsilon) = f. 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(epsilon) of solutions converges weakly to u in W-1,W-p and the gradients D(x)u(epsilon) 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.

potential

homogenization

nonlinear

Författare

Hermann Douanla Yonta

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Nils Svanstedt

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Applicable Analysis

0003-6811 (ISSN) 1026-7360 (eISSN)

Vol. 91 1205-1218

Ämneskategorier

Matematik

DOI

10.1080/00036811.2012.670225