Density of continuous functions in Sobolev spaces with applications to capacity
Eriksson-Bique, S., & Poggi-Corradini, P. (2024). Density of continuous functions in Sobolev spaces with applications to capacity. Transactions of the American Mathematical Society : Series B, 11, 901-944. https://doi.org/10.1090/btran/188
Date
2024Copyright
© 2024 the Authors
We show that capacity can be computed with locally Lipschitz functions in locally complete and separable metric spaces. Further, we show that if (X, d, μ) is a locally complete and separable metric measure space, then continuous functions are dense in the Newtonian space N1,p (X). Here the measure μ is Borel and is finite and positive on all metric balls. In particular, we don’t assume properness of X, doubling of μ or any Poincaré inequali-ties. These resolve, partially or fully, questions posed by a number of authors, including J. Heinonen, A. Björn and J. Björn. In contrast to much of the past work, our results apply to locally complete spaces X and dispenses with the frequently used regularity assumptions: doubling, properness, Poincaré inequality, Loewner property or quasiconvexity.
Publisher
American Mathematical Society (AMS)ISSN Search the Publication Forum
2330-0000Keywords
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https://converis.jyu.fi/converis/portal/detail/Publication/233351160
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Research Council of FinlandFunding program(s)
Postdoctoral Researcher, AoFAdditional information about funding
The first author was partially supported by Finnish Academy Grants n. 345005 and n. 356861. The second author was partially supported by NSF DMS n. 2154032.License
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