Abstract
This paper proves two-sided estimates for the Dirichlet heat kernel on inner uniform domains in metric measure Dirichlet spaces satisfying the volume doubling condition, the Poincaré inequality, and a cutoff Sobolev inequality. More generally, we obtain local upper and lower bounds for the Dirichlet heat kernel on locally inner uniform domains under local geometric assumptions on the underlying space.
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28 September 2022
A Correction to this paper has been published: https://doi.org/10.1007/s11118-022-10038-5
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Acknowledgements
A major part of this work was done while the author was affiliated with the University of Illinois at Urbana-Champaign. Discussions with Naotaka Kajino are gratefully acknowledged.
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Lierl, J. The Dirichlet Heat Kernel in Inner Uniform Domains in Fractal-Type Spaces. Potential Anal 57, 521–543 (2022). https://doi.org/10.1007/s11118-021-09926-z
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DOI: https://doi.org/10.1007/s11118-021-09926-z