反自对偶拉格朗日迭代及其在哈密顿系统和多参数梯度流中的应用
Iterations of anti-selfdual Lagrangians and applications to Hamiltonian systems and multiparameter gradient flows
摘要：
只要在状态空间上加上适当的自对偶边界拉格朗日量，反自对偶拉格朗日量就可以提升到道路空间。这个过程可以通过将道路空间视为新获得的反自对偶拉格朗日量的新状态空间来迭代。我们在这里给这些显着的持久性性质的两个应用。在第一部分中，我们建立了在可能无限维的辛空间$H^2$上的某些凹凸Hamilton算子${\cal H}$，在给定的时间T>0内连接两个拉格朗日子流形的哈密顿系统$-J\dot u (t)=\partial {\cal H} (u(t))$的解的存在性。另一个应用是构造凸势的多参数梯度流。我们的方法是基于文[4]、[5]和[7]中发展的反自对偶拉格朗日量的新变分法。
英文摘要：
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].
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
