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On the domains of Dirichlet forms on metric measure spaces

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Abstract

We prove that the domain of the local Dirichlet form is strictly contained in the domain of any stable-like non-local Dirichlet form on general metric measure spaces. We construct explicit functions in the difference of the domains of the Dirichlet forms on the Sierpiński gasket and the Sierpiński carpet.

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  1. Meng Yang

    Present address: Centro de Matemática e Aplicações, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Quinta da Torre, 2829-516, Caparica, Portugal

Authors and Affiliations

  1. Université Grenoble Alpes, CNRS UMR 5582, Institut Fourier, Gières, France

    Meng Yang

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  1. Meng Yang
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The author was supported by SFB1283 of the German Research Council (DFG). This work was partly supported by the French ANR project RAGE ANR-18-CE40-0012. This work is funded by national funds through the FCT—Fundação para a Ciência e a Tecnologia, I.P., under the scope of the project UIDB/00297/2020 (Center for Mathematics and Applications). The author was very grateful to Dr. Eryan Hu for helpful discussions. The author was very grateful to anonymous suggestions to generalize to general metric measure spaces.

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Yang, M. On the domains of Dirichlet forms on metric measure spaces. Math. Z. 301, 2129–2154 (2022). https://doi.org/10.1007/s00209-022-02987-9

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  • DOI: https://doi.org/10.1007/s00209-022-02987-9

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