Asymptotic Analysis - Volume 2, issue 1

Authors: Malgrange, Bernard

Article Type: Research Article

DOI: 10.3233/ASY-1989-2101

Citation: Asymptotic Analysis, vol. 2, no. 1, pp. 1-4, 1989

Authors: Huet, Denise

Article Type: Research Article

Abstract: It is shown that Sobolev spaces with two indices Hs ε (X), s=(s1 ,s2 )∈R2 are proper approximations of usual Sobolev spaces HS1 (X). It is also stated that, under natural conditions, an estimate of the form ‖u‖Hε ≤C{‖Aε u‖Fε +‖u‖Eε } for an operator Aε from a space Hε to a space Fε can be sharpened and can lead to the inverse stability of Aε . Under minimal assumptions on the data, these results can be used for establishing convergence results for solutions of classical or Wiener–Hopf coercive singularly perturbed problems …investigated by Frank and Wendt [10,11,12,37,38] and for solutions of boundary value problems in Lp -spaces. Show more

DOI: 10.3233/ASY-1989-2102

Citation: Asymptotic Analysis, vol. 2, no. 1, pp. 5-19, 1989

Authors: Defranceschi, Anneliese

Article Type: Research Article

Abstract: The paper deals with equations of the form −div(a(x,Du))=f, where a(x,ξ) is cyclically monotone. The main result is that, given a sequence ah of maximal monotone operators of this type, the convergence of the sequence of the solutions uh to the equations −div(ah (x,Duh ))=fh implies the convergence of the corresponding momenta ah (x,Duh ) in spite of the fact that the functions ah are nonlinear. The equivalence between the Γ-convergence of certain integral functionals and the G-convergence of the corresponding sub differentials is also established.

DOI: 10.3233/ASY-1989-2103

Citation: Asymptotic Analysis, vol. 2, no. 1, pp. 21-37, 1989

Authors: Ramis, J.-P. | Sibuya, Y.

Article Type: Research Article

DOI: 10.3233/ASY-1989-2104

Citation: Asymptotic Analysis, vol. 2, no. 1, pp. 39-94, 1989