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Rate of convergence in singular perturbations

Wilfred M. Greenlee — 1968

Annales de l'institut Fourier

Soit $D \subset R^{n}$ un domaine et $ϵ$ un paramètre réel positif. Considérons les deux problèmes aux limites sur $D$ , $(ϵ 𝒰 + ℬ w_{ϵ} = f$ et $ℬ u = f$ , où $𝒰$ et $ℬ$ sont des opérateurs différentiels elliptiques et où le degré de $𝒰$ est supérieur au degré de $ℬ$ . En utilisant l’interpolation quadratique entre espaces de Hilbert, on étudie les problèmes suivants : 1) Déterminer les normes pour lesquelles $w_{ϵ}$ converge vers $u$ ; 2) Estimer la rapidité de convergence de $w_{ϵ}$ vers $u$ , pour ces normes.

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