Celebratio Mathematica — Choquet-Bruhat

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Works connected to Alice Chaljub-Simon

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A. Chaljub-Simon and Y. Choquet-Bruhat: “Solutions asymptotiquement euclidiennes de l’équation de Lichnerowicz,” C. R. Acad. Sci. Paris Sér. A-B 286 : 20 (1978), pp. A917–A920. This paper is related to a later paper published in English by the same authors: “Global solutions of the Lichnerowicz equation in {G}eneral {R}elativity on an asymptotically {E}uclidean complete manifold,” General Relativity and Gravity 12 (1980). MR 498871 Zbl 0388.35006 article

A. Chaljub-Simon and Y. Choquet-Bruhat: “Problèmes elliptiques du second ordre sur une variété euclidienne à l’infini,” Ann. Fac. Sci. Toulouse Math. (5) 1 : 1 (1979), pp. 9–25. MR 533596 Zbl 0411.35044 article

A. Chaljub-Simon and Y. Choquet-Bruhat: “Solution de l’équation de Lichnerowicz sur une variété asymptotiquement euclidienne,” C. R. Acad. Sci. Paris Sér. A-B 288 : 16 (1979), pp. A779–A784. MR 535811 Zbl 0407.58038 article

A. Chaljub-Simon and Y. Choquet-Bruhat: “Global solutions of the Lichnerowicz equation in general relativity on an asymptotically Euclidean complete manifold,” Gen. Relativity Gravitation 12 : 2 (1980), pp. 175–185. MR 575238 article

We prove some existence and uniqueness theorems for the solution of the Liehnerowicz equation: \[ 8\Delta_g \phi - R\phi + M\phi^{-7} + \mathcal{Q}\phi^{-3} + \tau \phi^{5} = 0 ,\] on an asymptotically Euclidian manifold. This equation governs the conformal factor of a metric solution of the constraints in General Relativity. In the first part we prove existence and uniqueness under the simple assumption \( R\geq 0 \), \( M\geq 0 \), \( \mathcal{Q} \geq 0 \), \( \tau \geq 0 \), which insures the monotony of the non-differentiated part. In the second part we obtain an existence theorem under more general hypothesis on the co-efficients, by use of the Leray–Schauder degree theory. The results of this paper have been announced in [Chaljub-Simon and Choquet-Bruhat 1978].