摘要:

In classical point particle mechanics, Hamilton-Jacobi equation (in Euclidean space) gives a dual formulation of Newtonian dynamics, at least in a formal sense. In continuum mechanics, such relation translates to become Hamilton-Jacobi equation in space of probability measures and compressible Euler equations. In the case of Newtonian attractive potential, the Hamiltonian can become H=infinity - infinity. This talk is concerned with a notion of solution which we can develop well-posedness for the Hamilton-Jacobi equation in space of probability measures. In fact, what is essential is the metric nature of the problem. Hence the discuss will take place in complete metric space with length property.

Joint work with Luigi Ambrosio, Scuola Normale Superiori di Pisa.