On a Class of First Order Hamilton-jacobi Equations in Metric Spaces

  title={On a Class of First Order Hamilton-jacobi Equations in Metric Spaces},
  author={Luigi Ambrosio},
We establish well-posedness of a class of first order Hamilton-Jacobi equation in geodesic metric spaces. The result is then applied to solve a Hamilton-Jacobi equation in the Wasserstein space of probability measures, which arises from the variational formulation of a compressible Euler equation. 

From This Paper

Topics from this paper.


Publications referenced by this paper.
Showing 1-10 of 27 references

Gradient flows

  • L. Ambrosio, N. Gigli, G. Savaré
  • Second edition, Lectures in Mathematics ETH Z…
  • 2008
Highly Influential
14 Excerpts

On the geometry of the space of probability measures endowed with the quadratic optimal transportation distance Ph.D

  • N. Gigli
  • Thesis, Scuola Normale Superiore,
  • 2008
Highly Influential
9 Excerpts

Hamilton-Jacobi equations in space of measures associated with a system of conservation laws

  • J. Feng, T. Nguyen
  • J. Math. Pures Appl. (9)
  • 2012
Highly Influential
10 Excerpts

Large deviation for stochastic processes Mathematical Survey and Monographs, American Mathematical Society, Vol

  • J. Feng, T. G. Kurtz
  • 131, Rhode Island,
  • 2006
Highly Influential
5 Excerpts

Lions. Hamilton-Jacobi Equations in Infinite Dimensions

  • M. G. Crandall, P.L
  • PART I J. Funct. Anal
  • 1985
Highly Influential
6 Excerpts

Optimal transport

  • C. Villani
  • Classe di Scienze,
  • 2009
Highly Influential
3 Excerpts

Similar Papers

Loading similar papers…