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Sharp boundary trace inequalities

Published online by Cambridge University Press:  30 January 2014

Giles Auchmuty
Giles Auchmuty*
Affiliation:
Department of Mathematics, University of Houston, Houston, TX 77204-3008, USA (auchmuty@uh.edu)
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Abstract

This paper describes sharp inequalities for the trace of Sobolev functions on the boundary of a bounded region Ω ⊂ ℝN. The inequalities bound (semi-)norms of the boundary trace by certain norms of the function, its gradient on the region and by two specific constants κρ and κΩ associated with the domain and a weight function, respectively. These inequalities are sharp in that there exist functions for which equality holds. Explicit inequalities in some special cases when the region is a ball, or the region between two balls, are evaluated.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 144 , Issue 1 , February 2014 , pp. 1 - 12
Copyright
Copyright © Royal Society of Edinburgh 2014 

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