Stabilité et convergence dans les problèmes de perturbation singulière

Article type: Research Article

Authors: Huet, Denise

Affiliations: Département de Mathématique, Université de Nancy I, 86 rue Félix Faure, 54000 Nancy, France

Abstract: It is shown that Sobolev spaces with two indices Hsε(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{‖Aεu‖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.

DOI: 10.3233/ASY-1989-2102

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