Non-doubling ahlfors measures, perimeter measures, and the characterization of the trace spaces of sobolev functions in carnot-carathéodory spaces

Donatella Danielli, Nicola Garofalo, Duy Minh Nhieu

Research output: Contribution to journalArticlepeer-review

58 Scopus citations

Abstract

The object of the present study is to characterize the traces of the Sobolev functions in a sub-Riemannian, or Carnot-Carathéodory space. Such traces are defined in terms of suitable Besov spaces with respect to a measure which is concentrated on a lower dimensional manifold, and which satisfies an Ahlfors type condition with respect to the standard Lebesgue measure. We also study the extension problem for the relevant Besov spaces. Various concrete applications to the setting of Carnot groups are analyzed in detail and an application to the solvability of the subelliptic Neumann problem is presented.

Original languageEnglish (US)
Pages (from-to)1-124
Number of pages124
JournalMemoirs of the American Mathematical Society
Volume182
Issue number857
DOIs
StatePublished - Jul 2006
Externally publishedYes

Keywords

  • Besov spaces
  • Extension
  • Perimeter measures
  • Restriction
  • Sub-elliptic Sobolev spaces
  • Traces

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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