Characterizations of Sobolev Functions that vanish on a part of the boundary

Moritz Egert; Patrick Tolksdorf

Characterizations of Sobolev Functions that vanish on a part of the boundary

Classical Analysis and ODEs 2016-09-20 v1

Authors: Moritz Egert , Patrick Tolksdorf

Abstract

Let $\Omega$ be a bounded domain in R n with a Sobolev extension property around the complement of a closed part D of its boundary. We prove that a function u $\in$ W 1,p ( $\Omega$ ) vanishes on D in the sense of an interior trace if and only if it can be approximated within W 1,p ( $\Omega$ ) by smooth functions with support away from D. We also review several other equivalent characterizations, so to draw a rather complete picture of these Sobolev functions vanishing on a part of the boundary.

Keywords

Sobolev functions boundary trace Sobolev extension property function approximation interior trace

Cite

@article{arxiv.1609.05749,
  title  = {Characterizations of Sobolev Functions that vanish on a part of the boundary},
  author = {Moritz Egert and Patrick Tolksdorf},
  journal= {arXiv preprint arXiv:1609.05749},
  year   = {2016}
}

Comments

PDE 2015 -- Theory and Applications of Partial Differential Equations, Nov 2015, Berlin, Germany. PDE 2015: Conference Proceedings -- Special Issue of Discrete and Continuous Dynamical Systems - Series S

Characterizations of Sobolev Functions that vanish on a part of the boundary

Abstract

Keywords

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