C. R. Math. Rep. Acad. Sci. Canada Vol. 30 (3) 2008, pp. 65–83
September 30, 2008
Nassif Ghoussoub, Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2; email: nassif@math.ubc.ca
Abbas Moameni, Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2; email: moameni@math.ubc.ca
Abstract/Résumé:
We use a new variational method—based on the theory of anti-selfdual Lagrangians developed recently—to establish the existence of solutions of convex Hamiltonian systems that connect two given Lagrangian submanifolds in \(\mathbb{R}^{2N}\). We also consider the case where the Hamiltonian is only semi-convex. A variational principle is also used to establish existence for the corresponding Cauchy problem.
Une nouvelle méthode variationnelle—basée sur la théorie des Lagrangiens auto-adjoints developée récemment—est utilisée pour établir l’existence de solutions de systèmes Hamiltoniens convexes, qui connectent deux sous-variétés Lagrangiennes données dans \(\mathbb{R}^{2N}\). On considère aussi le cas des Hamiltoniens semi-convexes, ainsi que le problème de Cauchy correspondant.
[AMS Subject Classification: Hamiltonian structures; symmetries; variational principles; conservation laws 37K05
[This journal is open access except for the current year and the preceding 5 years]