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A sharp trace inequality for functions of bounded variation in the ball

Published online by Cambridge University Press:  27 November 2012

Andrea Cianchi
Andrea Cianchi*
Affiliation:
Dipartimento di Matematica ‘U. Dini’, Università di Firenze, Piazza Ghiberti 27, 50122 Firenze, Italy (cianchi@unifi.it)
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Abstract

The best constant in a mean-value trace inequality for functions of bounded variation on admissible domains Ω ⊂ ℝn is shown to agree with an isoperimetric constant associated with Ω. The existence and form of extremals is also discussed. This result is exploited to compute the best constant in the relevant trace inequality when Ω is a ball. The existence and the form of extremals in this special case turn out to depend on the dimension n. In particular, the best constant is not achieved when Ω is a disc in ℝ2.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 142 , Issue 6 , December 2012 , pp. 1179 - 1191
Copyright
Copyright © Royal Society of Edinburgh 2012

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