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Homogenization of a nonlinear elliptic problem with large nonlinear potential

Hermann Douanla (Institutionen för matematiska vetenskaper, matematik) ; Nils Svanstedt (Institutionen för matematiska vetenskaper, matematik)
Applicable Analysis (0003-6811). Vol. 91 (2012), 6, p. 1205-1218.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: nonlinear, potential, homogenization

Denna post skapades 2012-06-18. Senast ändrad 2017-07-03.
CPL Pubid: 159112


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Institutionen för matematiska vetenskaper, matematik (2005-2016)



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