TITLE

Iterations of anti-selfdual Lagrangians and applications to Hamiltonian systems and multiparameter gradient flows

AUTHOR(S)
Ghoussoub, Nassif; Tzou, Leo
PUB. DATE
August 2006
SOURCE
Calculus of Variations & Partial Differential Equations;Aug2006, Vol. 26 Issue 4, p511
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
Anti-selfdual Lagrangians on a state space lift to path space provided one adds a suitable selfdual boundary Lagrangian. This process can be iterated by considering the path space as a new state space for the newly obtained anti-selfdual Lagrangian. We give here two applications for these remarkable permanence properties. In the first, we establish for certain convex�concave Hamiltonians $${\cal H}$$ on a�possibly infinite dimensional�symplectic space H 2, the existence of a solution for the Hamiltonian system $$-J\dot u (t)\in \partial {\cal H}(u(t))$$ that connects in a given time T > 0, two Lagrangian submanifolds. Another application deals with the construction of multiparameter flows, including those generated by vector fields that represent superpositions of skew-adjoint operators with gradients of convex potentials. Our methods are based on the new variational calculus for anti-selfdual Lagrangians developed in [5�7].
ACCESSION #
20924997

 

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