Rate of convergence in singular perturbations

Greenlee, Wilfred M.

Annales de l'Institut Fourier, Tome 18 (1968) no. 2, pp. 135-191.

Soit $D\subset {\mathbf{R}}^n$ un domaine et $\epsilon$ un paramètre réel positif. Considérons les deux problèmes aux limites sur $D$, $(\epsilon 𝒰+ℬw_{\epsilon }=f$ et $ℬu=f$, 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 $w_{\epsilon }$ converge vers $u$ ;

2) Estimer la rapidité de convergence de $w_{\epsilon }$ vers $u$, pour ces normes.

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