A duality-based approach to gradient flows of linear growth functionals

• Górny, Wojciech ^[1] ; Mazón, José M. ^[2]
  1. [1] University of Vienna

     University of Vienna

     Innere Stadt, Austria

     
  2. [2] Universitat de València

     Universitat de València

     Valencia, España

     
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 69, Nº 2, 2025, págs. 341-365
• Idioma: inglés
• DOI: 10.5565/publmat6922504
• Enlaces
  • Texto completo
• Resumen

  • We study gradient flows of general functionals with linear growth with very weak assumptions. Classical results concerning characterisation of solutions require differentiability of the Lagrangian, as for the time-dependent minimal surface equation, or a special form of the Lagrangian as in the total variation flow. We propose to study this problem using duality techniques, give a general definition of solutions, and prove their existence and uniqueness. This approach also allows us to reduce the regularity and structure assumptions on the Lagrangian.

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