We study the structure of Sobolev spaces on the cartesian/warped products of a given metric measure space and an interval. Our main results are: – the characterization of the Sobolev spaces in such products,– the proof that, under natural assumptions, the warped products possess the Sobolev-to-Lipschitz property, which is key for geometric applications.The results of this paper have been needed in the recent proof of the ‘volume-cone-to-metric-cone’ property of RCD spaces obtained by the first author and De Philippis.

Sobolev spaces on warped products / Gigli, Nicola; Han, Bang-Xian. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - 275:8(2018), pp. 2059-2095. [10.1016/j.jfa.2018.03.021]

Sobolev spaces on warped products

Gigli, Nicola
;
2018

Abstract

We study the structure of Sobolev spaces on the cartesian/warped products of a given metric measure space and an interval. Our main results are: – the characterization of the Sobolev spaces in such products,– the proof that, under natural assumptions, the warped products possess the Sobolev-to-Lipschitz property, which is key for geometric applications.The results of this paper have been needed in the recent proof of the ‘volume-cone-to-metric-cone’ property of RCD spaces obtained by the first author and De Philippis.
275
8
2059
2095
https://www.sciencedirect.com/science/article/pii/S0022123618301381?via%3Dihub
Gigli, Nicola; Han, Bang-Xian
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11767/88145
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