Boundary behavior of functions from Sobolev classes defined on domains with exterior peak

M. Yu. Vasil'chik, I. M. Pupyshev<sup>a

a</sup> Novosibirsk State Technical University, Novosibirsk, Russia

Abstract: We establish an invertible characteristic of the boundary behavior of functions from Sobolev spaces defined on a space domain having a vertex of exterior peak on the boundary. The boundary is assumed sufficiently smooth in a neighborhood of the peak vertex. The description of the traces on the boundary is given with the use of weighted Besov spaces.

Key words: Sobolev space, weighted Besov space, peak, boundary behavior of functions.

UDC: 517.518.234

Received: 18.08.2013

 English version: Siberian Advances in Mathematics, 2014, 24:4, 261–281

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