Search
Talk

On Lebesgue points of entropy solutions to the 2D eikonal equation

  • Xavier Lamy (Université Paul Sabatier, Toulouse)
E1 05 (Leibniz-Saal)

Abstract

Entropy solutions of the 2D eikonal equation arise as limits of sequences of bounded Aviles-Giga energy. They might be much less regular than viscosity solutions, which have BV gradient, nevertheless their gradients share several structural properties with BV maps, as discovered by De Lellis and Otto. Fine estimates on their Lebesgue points are however still open. In a joint work with Elio Marconi, we obtain a bound on local oscillations in terms of the entropy production, implying in particular that non-Lebesgue points have codimension 1 (as they would for BV maps).

Katja Heid

MPI for Mathematics in the Sciences Contact via Mail

Upcoming Events of This Seminar

  • Mar 12, 2024 tba with Theresa Simon
  • Mar 26, 2024 tba with Phan Thành Nam
  • Mar 26, 2024 tba with Dominik Schmid
  • May 7, 2024 tba with Manuel Gnann
  • May 14, 2024 tba with Barbara Verfürth
  • May 14, 2024 tba with Lisa Hartung
  • Jun 25, 2024 tba with Paul Dario
  • Jul 16, 2024 tba with Michael Loss