The~Sobolev--Poincar\'e inequality and the~$L_{q,p}$-cohomology of~twisted cylinders

V. Gol'dstein ; Ya. A. Kopylov

Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 566-584.

Résumé

We establish a vanishing result for the $L_{q,p}$-cohomology (${q\ge p}$) of a twisted cylinder, which is a generalization of a warped cylinder. The result is new even for warped cylinders. We base on the methods for proving the $(p,q)$-Sobolev–Poincaré inequality developed by L. Shartser.

Détail

Keywords: differential form, Sobolev–Poincaré inequality, $L_{q,p}$-cohomology, twisted cylinder, homotopy operator.

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