[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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