Topological Methods in Nonlinear Analysis

Constants of motion for non-differentiable quantum variational problems

Jacky Cresson, Gastão S. F. Frederico, and Delfim F. M. Torres

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We extend the DuBois-Reymond necessary optimality condition and Noether's symmetry theorem to the scale relativity theory setting. Both Lagrangian and Hamiltonian versions of Noether's theorem are proved, covering problems of the calculus of variations with functionals defined on sets of non-differentiable functions, as well as more general non-differentiable problems of optimal control. As an application we obtain constants of motion for some linear and nonlinear variants of the Schrödinger equation.

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Topol. Methods Nonlinear Anal., Volume 33, Number 2 (2009), 217-231.

First available in Project Euclid: 27 April 2016

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Cresson, Jacky; Frederico, Gastão S. F.; Torres, Delfim F. M. Constants of motion for non-differentiable quantum variational problems. Topol. Methods Nonlinear Anal. 33 (2009), no. 2, 217--231.

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