Proximal Aiming in Weak KAM Theory with Nonsmooth Lagrangian
Abstract
Abstract This work extends weak KAM theory to the case of a nonsmooth Lagrangian satisfying a superlinear growth condition. By combining a solution of a weak KAM equation, which is a stationary Hamilton–Jacobi equation, with the proximal aiming method, we construct a family of discontinuous feedback strategies that are nearly optimal on every time interval. This result yields an analog of the weak KAM theorem. Furthermore, as in classical weak KAM theory, we demonstrate that the effective Hamiltonian (Mañé critical value) can be determined by solving a linear programming problem in the class of probability measures.
Fields of Study & Subjects
Black Holes and Theoretical Physics
Quantum chaos and dynamical systems
Quantum Chromodynamics and Particle Interactions
Publication details
- Journal / source
- Proceedings of the Steklov Institute of Mathematics
- Publisher
- Pleiades Publishing Ltd
- Volume
- 332
- Issue
- 1
- Pages
- 1–17
- Publication date
- 1 March 2026
- Language
- EN