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A priori bounds and renormalized Morse indices of solutions of an elliptic system

✍ Scribed by Sigurd B Angenent; Robertus van der Vorst

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
198 KB
Volume
17
Category
Article
ISSN
0294-1449

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✦ Synopsis

We define a "renormalized" Morse index, and prove a Bahri-Lions type result for critical points of E(u, v) = Ω {∇u • ∇v -H (x, u, v)} dx; i.e., we establish an a priori bound for critical points with bounded Morse index. © 2000 Éditions scientifiques et médicales Elsevier SAS RÉSUMÉ. -Nous définissons un indice de Morse généralisé pour les points critiques de la fonction

Le but principal de ce travail est la démonstration d'une estimation de type Bahri-Lions [2] pour les points critiques. Nous montrons pour chaque entier m ∈ N que l'ensemble des points critiques dont l'indice renormalisé µ satisfait µ m est borné dans L ∞ (Ω) × L ∞ (Ω).

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