Asymptotic analysis of boundary value problems for quasi-linear monotone operators

Article type: Research Article

Authors: Defranceschi, Anneliese

Affiliations: SISSA, Strada Costiera 11, 34014 Trieste, Italy

Note: [] Permanent address: Università degli Studi di Trento, Dip. di Matematica, I-38050 Povo, Italy.

Abstract: By means of the notion of G-convergence introduced in [4] we deal with the limit behaviour, as h→+∞, of the solutions uh to Neumann boundary value problems for quasi-linear monotone operators of the form Ahu=−div(ah(x,Duh)), and we also include in our analysis more general linear boundary conditions. Furthermore, we extend the homogenization result obtained in [6] to this case and the corresponding correctors studied in [7]. Finally, we deal with the asymptotic behaviour, as h→+∞, of the solutions uh to quasi-linear equations −div(ah(x,Duh))=f on perforated domains Ωh⊆Ω of Rn with homogeneous Neumann boundary conditions on the holes, when the regularity assumptions on ah required in [5] are dropped.

DOI: 10.3233/ASY-1990-3303

Journal: Asymptotic Analysis, vol. 3, no. 3, pp. 221-247, 1990