Since the beginning of Calculus of Variations the classical Bolza problem has been widely studied not only in an Euclidean space but also in a Riemannian manifold. Recently, it has been completely solved if the Lagrangian is ${\cal L}(s,x,v) = \langle v,v \rangle/2 - V(x,s)$, with potential $V$ which grows at most quadratically at infinity with respect to $x$, and its solutions have been related to geodesics in gravitational waves.
Old Bolza problem and its new links to General Relativity
CANDELA, Anna Maria
2004-01-01
Abstract
Since the beginning of Calculus of Variations the classical Bolza problem has been widely studied not only in an Euclidean space but also in a Riemannian manifold. Recently, it has been completely solved if the Lagrangian is ${\cal L}(s,x,v) = \langle v,v \rangle/2 - V(x,s)$, with potential $V$ which grows at most quadratically at infinity with respect to $x$, and its solutions have been related to geodesics in gravitational waves.File in questo prodotto:
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