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
;
2018-01-01
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.| File | Dimensione | Formato | |
|---|---|---|---|
|
Warped-Product-Space.pdf
Open Access dal 17/10/2019
Tipologia:
Documento in Post-print
Licenza:
Creative commons
Dimensione
387.09 kB
Formato
Adobe PDF
|
387.09 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
