Search
Talk

The 1-harmonic flow

  • Lorenzo Giacomelli (Università di Roma 'La Sapienza')
Felix-Klein-Hörsaal Universität Leipzig (Leipzig)

Abstract

The $1$-harmonic flow is the formal gradient flow --with respect to the $L^2$-distance-- of the total variation of a manifold-valued unknown function. The problem originates from image processing and has an intrinsic analytical interest as prototype of constrained and vector-valued evolution equations in $BV$-spaces. I will introduce a notion of solution and I will present existence (and, in some cases, uniqueness) results when the target manifold is either the hyper-octant of a sphere or a connected subarc of a regular Jordan curve. I will also discuss a work in progress concerning local/global-in-time well-posedness in Lipschitz spaces. As all of the above is just a first, tentative step into a rather uncharted territory, I will conclude by highlighting a few basic open questions.

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