共查询到7条相似文献,搜索用时 15 毫秒
1.
We study the asymptotic behaviour of non-negative solutions of Yamabe type equations on a complete Riemannian manifold. Then we provide a comparison result, based on a form of the weak maximum principle at infinity, which together with the “a priori” estimates previously obtained, yields uniqueness under very general Ricci assumptions. The paper ends with an existence result and an application to the non-compact Yamabe problem. 相似文献
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Amel Atallah 《Transactions of the American Mathematical Society》2000,352(6):2701-2721
RÉSUMÉ. On considère dans un ouvert borné de , à bord régulier, le problème de Dirichlet
où , est positive et s'annule sur un ensemble fini de points de . On démontre alors sous certaines hypothèses sur et si est assez petit, que le problème (1) possède une solution convexe unique .
ABSTRACT. We consider in a bounded open set of , with regular boundary, the Dirichlet problem
where , is positive and vanishes on , a finite set of points in . We prove, under some hypothesis on and if is sufficiently small, that the problem (1) has a unique convex solution .
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We correct in this note a mistake in [Delort, J.-M., Existence globale et comportement asymptotique pour l'équation de Klein-Gordon quasi linéaire à données petites en dimension 1, Ann. Sci. École Norm. Sup. (4) 34 (1) (2001) 1-61], which has been indicated to us by H. Lindblad. The results of [Delort, J.-M., Existence globale et comportement asymptotique pour l'équation de Klein-Gordon quasi linéaire à données petites en dimension 1, Ann. Sci. École Norm. Sup. (4) 34 (1) (2001) 1-61] still hold true if one increases the smoothness assumption made on the Cauchy data. 相似文献
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Gabriele Grillo Matteo Muratori Fabio Punzo 《Journal of Differential Equations》2019,266(7):4305-4336
We consider the porous medium equation with power-type reaction terms on negatively curved Riemannian manifolds, and solutions corresponding to bounded, nonnegative and compactly supported data. If , small data give rise to global-in-time solutions while solutions associated to large data blow up in finite time. If , large data blow up at worst in infinite time, and under the stronger restriction all data give rise to solutions existing globally in time, whereas solutions corresponding to large data blow up in infinite time. The results are in several aspects significantly different from the Euclidean ones, as has to be expected since negative curvature is known to give rise to faster diffusion properties of the porous medium equation. 相似文献
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We give a stochastic interpretation of the geometrical representation, from E. Cartan, of the heat equation, in terms of ideal exterior differential forms and isovectors generating the symmetries of this equation. The method can also be used to interpret as a stochastic deformation the contact geometry of first order ordinary differential equations and the search for infinitesimal symmetries of the associated Hamilton–Jacobi equation. We thus generalise, in an elegant and geometrical way, the results coming originally from long calculations of stochastic analysis. To cite this article: P. Lescot, J.-C. Zambrini, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 263–266. 相似文献
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Hong-Quan Li Noë l Lohoue 《Transactions of the American Mathematical Society》2003,355(2):689-711
We prove R. Strichartz's estimates for solutions of the wave equation on some conical manifolds. RÉSUMÉ. On prouve des estimations pour les solutions de l'équation des ondes, analogues aux estimations de R. Strichartz, sur certaines variétés coniques.