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This article is cited in 16 scientific papers (total in 16 papers)
Coercive estimates and integral representation formulas on Carnot groups
D. V. Isangulovaa, S. K. Vodopyanovb a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
b Mechanics and Mathematics Department, Novosibirsk State University, Novosibirsk, Russia
Abstract:
For general Carnot groups, we obtain coercive estimates for homogeneous differential operators with
constant coefficients, kernels of which have finite dimension. We develop new Sobolev-type integral representations of differentiable functions which are a crucial tool for deriving coercive estimates. Moreover we prove some auxiliary results having independent interest, in particular, Sobolev type embedding and compactness theorems for John domains.
Keywords and phrases:
coercive estimate, integral representation, Sobolev space, Carnot group.
Received: 15.06.2010
Citation:
D. V. Isangulova, S. K. Vodopyanov, “Coercive estimates and integral representation formulas on Carnot groups”, Eurasian Math. J., 1:3 (2010), 58–96
Linking options:
https://www.mathnet.ru/eng/emj29 https://www.mathnet.ru/eng/emj/v1/i3/p58
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Abstract page: | 511 | Full-text PDF : | 139 | References: | 48 |
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