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Шестая международная конференция по дифференциальным и функционально-дифференциальным уравнениям DFDE-2011
19 августа 2011 г. 12:55, г. Москва
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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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Количество просмотров: |
Эта страница: | 150 | Видеофайлы: | 92 |
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Аннотация:
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 $d$ is in general not differentiable, we will show that the vector field $d$ has enough regularity to allow a change of variable formula.
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 $H$ is uniformly convex, we will show that the solution is not only semiconcave, but its first derivative is SBV.
We will also consider the hyperbolic system
$$
u_t+f(u)_x=0
$$
and show that the direction of the characteristics are SBV.
Язык доклада: английский
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