Generalized characteristics and Lax-Oleinik operators: global theory

2016/05/24 by Cannarsa, Piermarco, Cheng, Wei · 2 citations
#Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1605.07581

Abstract

For autonomous Tonelli systems on \Rⁿ, we develop an intrinsic proof of the existence of generalized characteristics using sup-convolutions. This approach, together with convexity estimates for the fundamental solution, leads to new results such as the global propagation of singularities along generalized characteristics.

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• Global propagation of singularities for magnetic mechanical systems
• Optimal semiconcavity with fractional modulus for Hamilton-Jacobi equations with Neumann boundary conditions

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