This paper studies the structure of the singular set (points of nondifferentiability) of viscosity solutions to Hamilton-Jacobi equations associated with general mechanical systems on the n-torus. First, using the level set method, we characterize the propagation of singularities along generalized characteristics. Then, we obtain a local propagation result for singularities of weak KAM solutions in the supercritical case. Finally, we apply such a result to study the propagation of singularities for barrier functions.

Cannarsa, P., Cheng, W., Zhang, Q. (2014). Propagation of Singularities for Weak KAM Solutions and Barrier Functions. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 331(1), 1-20 [10.1007/s00220-014-2106-x].

Propagation of Singularities for Weak KAM Solutions and Barrier Functions

CANNARSA, PIERMARCO;
2014-01-01

Abstract

This paper studies the structure of the singular set (points of nondifferentiability) of viscosity solutions to Hamilton-Jacobi equations associated with general mechanical systems on the n-torus. First, using the level set method, we characterize the propagation of singularities along generalized characteristics. Then, we obtain a local propagation result for singularities of weak KAM solutions in the supercritical case. Finally, we apply such a result to study the propagation of singularities for barrier functions.
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - Analisi Matematica
English
Con Impact Factor ISI
Hamilton-Jacobi equations, weak KAM theory, singularities, barrier function
Partially supported by the Natural Scientific Foundation of China (Grant No. 11271182) and the National Basic Research Program of China (Grant No. 2013CB834100).
Cannarsa, P., Cheng, W., Zhang, Q. (2014). Propagation of Singularities for Weak KAM Solutions and Barrier Functions. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 331(1), 1-20 [10.1007/s00220-014-2106-x].
Cannarsa, P; Cheng, W; Zhang, Q
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/122516
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