Traces of Sobolev functions on the Ahlfors sets of Carnot groups |
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Authors: | S K Vodop’yanov I M Pupyshev |
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Institution: | (1) Sobolev Institute of Mathematics, Novosibirsk, Russia |
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Abstract: | We prove the converse of the trace theorem for the functions of the Sobolev spaces W p l 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. |
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Keywords: | Carnot group Sobolev space embedding theorem trace of a function extension of functions Whitney’ s theorem |
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