Strongly norm-attaining Lipschitz maps

  1. Chiclana Vega, Rafael
Dirigée par:
  1. Miguel Martín Suárez Directeur

Université de défendre: Universidad de Granada

Fecha de defensa: 18 mars 2021

Jury:
  1. Gilles Godefroy President
  2. Ginés López Pérez Secrétaire
  3. Rafael Payá Albert Rapporteur
  4. Gilles Lancien Rapporteur
  5. Eva Pernecká Rapporteur
Département:
  1. ANÁLISIS MATEMÁTICO

Type: Thèses

Teseo: 649135 DIALNET lock_openDIGIBUG editor

Résumé

We study the possibility of approximating every Lipschitz map by Lipschitz maps which attain their Lipschitz constant. That is, we study the denseness of the set LipSNA(M, Y) of strongly norm-attaining Lipschitz maps in the space Lip0(M; Y ) of all Lipschitz maps from a (complete pointed) metric space M to a Banach space Y . A Lipschitz map f : M → Y is said to strongly attain its (Lipschitz) norm if there are distinct points p, q ∈ M