This article is cited in 1 paper

The Extension of Functions of Sobolev Classes Beyond the Boundary of the Domain on Carnot Groups

I. M. Pupyshev

Novosibirsk State Technical University

Abstract: We prove the theorem on extension of the functions of the Sobolev space $W^l_p(\Omega)$ which are defined on a bounded $(\varepsilon,\delta)$-domain $\Omega$ in a two-step Carnot group beyond the boundary of the domain of definition. This theorem generalizes the well-known extension theorem by P. Jones for domains of the Euclidean space.

Key words: Sobolev space, Carnot group, extension of functions beyond the boundary of the domain of definition.

UDC: 517.54+517.813.52

Received: 22.12.2006

 English version: Siberian Advances in Mathematics, 2008, 18:2, 124–141

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