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VIDEO LIBRARY |
Sixth International Conference on Differential and Functional Differential Equations DFDE-2011
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Regularity estimates for Hamilton–Jacobi equations and hyperbolic conservation laws S. Bianchini International School for Advanced Studies, Trieste, Italy |
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Abstract: Consider the Hamilton–Jacobi equation $$ u_t+H(\nabla u)=0 $$ with convex Hamiltonian. In spite of the fact that the Hamiltonian is only convex, and thus the characteristic vector field Applications of this fact are a proof of the Sudakov theorem in optimal transportation theory and a solution of a conjecture of Cellina. In the case where We will also consider the hyperbolic system $$ u_t+f(u)_x=0 $$ and show that the direction of the characteristics are SBV. Language: English |