[CvGmt News] Seminari Calcolo delle Variazioni

alberti at mail.dm.unipi.it alberti at mail.dm.unipi.it
Sun Feb 6 01:11:46 CET 2005


The Aronsson-Euler Equation for 1-dimensional Hamiltonians
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   Seminari di Calcolo delle Variazioni e Teoria Geometrica della Misura

   when: Wednesday, February 9, at 5.30 PM

   where: Departiment of Mathematics, Pisa (Sala Riunioni)

   speaker: Albert Fathi (ENS Lyon)

   title: The Aronsson-Euler Equation for 1-dimensional Hamiltonians

   abstract: In relation with the Hamilton-Jacobi equation H(x, D[x] u) =
   c, Craig Evans introduced the Aronsson-Euler equation
   $$
   -D_x^2 ( {\partial H\over\partial p}(xD_x u),
                   {\partial H\over\partial p}(xD_x u) )
   -\langle {\partial H\over\partial x}(xD_x u);
                 {\partial H\over\partial x}(xD_x u) \rangle
    =0 \ .
    $$
   He  showed  relations with weak KAM theory. Yifeng Yu has extended the
   work of Evans. In this joint work with Antonio Siconolfi, we study the
   1-dimensional  case.  We show by examples that the Aubry set cannot be
   the  uniqueness  set  for  this Aronsson-Euler equation. We describe a
   uniqueness set.

Reference: http://www.dm.unipi.it/~alberti/files/altrepagine/SeminarioCVGMT/home.html#future

You find this news in the cvgmt preprint server: http://cvgmt.sns.it/news/20050209/

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