This article is cited in 3 papers

Real, complex and functional analysis

The continuity of Sobolev functions on the hyperplanes

A. S. Romanov<sup>ab

a</sup> Novosibirsk State University, Pirogova str., 2, 630090, Novosibirsk, Russia
^b Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia

Abstract: We discuss some of the problems associated with continuous trace Sobolev functions on the sections of the $ n $-dimensional cube by hyperplanes.

Keywords: Sobolev space, embedding theorem, Hausdorff measure.

UDC: 517.51

MSC: 46E35

Received October 6, 2015, published November 18, 2015

DOI: 10.17377/semi.2015.12.069