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- Title
Traces of Sobolev functions on the Ahlfors sets of Carnot groups.
- Authors
Vodop'yanov, S. K.; Pupyshev, I. M.
- Abstract
We prove the converse of the trace theorem for the functions of the Sobolev spaces W on a Carnot group on the regular closed subsets called Ahlfors d-sets (the direct trace theorem was obtained in one of our previous publications). The theorem generalizes Johnsson and Wallin’s results for Sobolev functions on the Euclidean space. As a consequence we give a theorem on the boundary values of Sobolev functions on a domain with smooth boundary in a two-step Carnot group. We consider an example of application of the theorems to solvability of the boundary value problem for one partial differential equation.
- Subjects
SOBOLEV spaces; FUNCTION spaces; EMBEDDING theorems; BOUNDARY value problems; PARTIAL differential equations; MATHEMATICAL research
- Publication
Siberian Mathematical Journal, 2007, Vol 48, Issue 6, p961
- ISSN
0037-4466
- Publication type
Article
- DOI
10.1007/s11202-007-0099-9