Global properties of Dirichlet forms in terms of Green’s formula

Sebastian Haeseler, Matthias Keller, Daniel Lenz, Jun Masamune, Marcel Schmidt

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


We study global properties of Dirichlet forms such as uniqueness of the Dirichlet extension, stochastic completeness and recurrence. We characterize these properties by means of vanishing of a boundary term in Green’s formula for functions from suitable function spaces and suitable operators arising from extensions of the underlying form. We first present results in the framework of general Dirichlet forms on σ-finite measure spaces. For regular Dirichlet forms our results can be strengthened as all operators from the previous considerations turn out to be restrictions of a single operator. Finally, the results are applied to graphs, weighted manifolds, and metric graphs, where the operators under investigation can be determined rather explicitly, and certain volume growth criteria can be (re)derived.

Original languageEnglish
Article number124
JournalCalculus of Variations and Partial Differential Equations
Issue number5
Publication statusPublished - 2017 Oct 1
Externally publishedYes


  • 31C25

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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