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Homogenization of a nonlinear elliptic problem with large nonlinear potential

Författare och institution:
Hermann Douanla (Institutionen för matematiska vetenskaper, matematik, Chalmers/GU); Nils Svanstedt (Institutionen för matematiska vetenskaper, Chalmers/GU)
Publicerad i:
Applicable Analysis, 91 ( 6 ) s. 1205-1218
ISSN:
0003-6811
Publikationstyp:
Artikel, refereegranskad vetenskaplig
Publiceringsår:
2012
Språk:
engelska
Fulltextlänk:
Sammanfattning (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 -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.
Ämne (baseras på Högskoleverkets indelning av forskningsämnen):
NATURVETENSKAP ->
Matematik
Nyckelord:
nonlinear, potential, homogenization
Postens nummer:
159112
Posten skapad:
2012-06-18 12:11
Posten ändrad:
2016-07-07 15:45

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