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Global properties of Dirichlet forms in terms of Green's formula
| Title: | Global properties of Dirichlet forms in terms of Green's formula |
| Authors: | Haeseler, Sebastian Browse this author | | Keller, Matthias Browse this author | | Lenz, Daniel Browse this author | | Masamune, Jun Browse this author | | Schmidt, Marcel Browse this author |
| Issue Date: | Oct-2017 |
| Publisher: | Springer |
| Journal Title: | Calculus of variations and partial differential equations |
| Volume: | 56 |
| Issue: | 5 |
| Start Page: | 124 |
| Publisher DOI: | 10.1007/s00526-017-1216-7 |
| Abstract: | 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 sigma-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. |
| Rights: | The final publication is available at Springer via http://dx.doi.org/10.1007/s00526-017-1216-7 |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/71572 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 正宗 淳
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