Traces of Newtonian-Sobolev, Hajlasz-Sobolev, and BV functions on metric spaces

Panu Lahti ^[1] ; Xining Li ^[2] ; Zhuang Wang ^[3]
1. [1] Chinese Academy of Sciences
  
  Chinese Academy of Sciences
  
  China
2. [2] Sun Yat-sen University
  
  Sun Yat-sen University
  
  China
3. [3] Hunan Normal University
  
  Hunan Normal University
  
  China
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Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 22, Nº 3, 2021, págs. 1353-1383
Idioma: inglés
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Resumen
- We study the boundary traces of Newton-Sobolev, Haj lasz-Sobolev, and BV (bounded variation) functions. Assuming less regularity of the domain than is usually done in the literature, we show that all of these function classes achieve the same “boundary values”, which in particular implies that the trace spaces coincide provided that they exist. Many of our results seem to be new even in Euclidean spaces but we work in a more general complete metric space equipped with a doubling measure and supporting a Poincaré inequality.