Characterisation of weak solutions to gradient flows of general linear growth functionals

Wojciech Gorny (U of Vienna)

Feb 25. 2025, 11:00 — 11:50

We study gradient flows in $L^2$ of general convex and lower semicontinuous functionals with linear growth. Typical examples of such evolution equations are the time-dependent minimal surface equation and the total variation flow. Classical results concerning characterisation of solutions require a special form or differentiability of the Lagrangian; we apply a duality-based method to formulate a general definition of solutions, prove their existence and uniqueness, and reduce the regularity and structure assumptions on the Lagrangian. The talk is primarily based on a joint work with José M. Mazón.

Further Information
Venue:
ESI Boltzmann Lecture Hall
Recordings:
Recording
Associated Event:
Degenerate and Singular PDEs (Workshop)
Organizer(s):
Verena Bögelein (PLUS, Salzburg)
Ugo Gianazza (U of Pavia)
Juha Kinnunen (Aalto U)
Naian Liao (PLUS, Salzburg)