Notions of Dirichlet problem for functions of least gradient in metric measure spaces

Riikka Korte ^[1] ; Panu Lahti ^[4] ; Xining Li ^[2] ; Nageswari Shanmugalingam ^[3]
1. [1] Aalto University
  
  Aalto University
  
  Helsinki, Finlandia
2. [2] Sun Yat-sen University
  
  Sun Yat-sen University
  
  China
3. [3] University of Cincinnati
  
  University of Cincinnati
  
  City of Cincinnati, Estados Unidos
4. [4] niversity of Cincinnati, USA and University of Jyväskylä
Mostrar afiliaciones +
Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 35, Nº 6, 2019, págs. 1603-1648
Idioma: inglés
Texto completo no disponible (Saber más ...)
Resumen
- We study two notions of Dirichlet problem associated with BV energy minimizers (also called functions of least gradient) in bounded domains in metric measure spaces whose measure is doubling and supports a (1, 1)-Poincaré inequality. Since one of the two notions is not amenable to the direct method of the calculus of variations, we construct, based on an approach of Juutinen and Mazón-Rossi–De León, solutions by considering the Dirichlet problem for p-harmonic functions, p>1, and letting p→1. Tools developed and used in this paper include the inner perimeter measure of a domain.