In this paper we prove Morse index theorems for a big class of constrained variational problems on graphs. Such theorems are useful in various physical and geometric applications. Our formulas compute the difference of Morse indices of two Hessians related to two different graphs or two different sets of boundary conditions. Some applications such as the iteration formulas and lower bounds for the index are proved.
Index theorems for graph-parametrized optimal control problems / Agrachev, Andrei; Baranzini, Stefano; Beschastnyi, Ivan. - In: NONLINEARITY. - ISSN 0951-7715. - 36:5(2023), pp. 2792-2838. [10.1088/1361-6544/acc5d4]
Index theorems for graph-parametrized optimal control problems
Baranzini, Stefano
;
2023-01-01
Abstract
In this paper we prove Morse index theorems for a big class of constrained variational problems on graphs. Such theorems are useful in various physical and geometric applications. Our formulas compute the difference of Morse indices of two Hessians related to two different graphs or two different sets of boundary conditions. Some applications such as the iteration formulas and lower bounds for the index are proved.| File | Dimensione | Formato | |
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