Mathematics – Analysis of PDEs
Scientific paper
2005-04-01
Mathematics
Analysis of PDEs
20 pages. Updated versions --if any-- of this author's papers can be downloaded at http://www.pims.math.ca/~nassif/
Scientific paper
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 $-J\dot u (t)=\partial {\cal H} (u(t))$ that connects in a given time T>0, two Lagrangian submanifolds. Another application deals with the construction of a multiparameter gradient flow for a convex potential. Our methods are based on the new variational calculus for anti-selfdual Lagrangians developed in [4], [5] and [7].
Ghoussoub Nassif
Tzou Leo
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