Finsler metrics and action potentials
R Iturriaga, H Sánchez-Morgado - Proceedings of the American …, 2000 - ams.org
Proceedings of the American Mathematical Society, 2000•ams.org
We study the behavior of Mañé's action potential $\Phi _k $ associated to a convex
superlinear Lagrangian, for $ k $ bigger than the critical value $ c (L) $. We obtain growth
estimates for the action potential as a function of $ k $. We also prove that the action
potential can be written as $\Phi _k (x, y)= D_F (x, y)+ f (y)-f (x) $ where $ f $ is a smooth
function and $ D_F $ is the distance function associated to a Finsler metric. References
superlinear Lagrangian, for $ k $ bigger than the critical value $ c (L) $. We obtain growth
estimates for the action potential as a function of $ k $. We also prove that the action
potential can be written as $\Phi _k (x, y)= D_F (x, y)+ f (y)-f (x) $ where $ f $ is a smooth
function and $ D_F $ is the distance function associated to a Finsler metric. References
Abstract
We study the behavior of Mañé’s action potential associated to a convex superlinear Lagrangian, for bigger than the critical value . We obtain growth estimates for the action potential as a function of . We also prove that the action potential can be written as where is a smooth function and is the distance function associated to a Finsler metric. References
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