A sharp trace inequality for functions of bounded variation in the ball
2012 ◽
Vol 142
(6)
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pp. 1179-1191
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Keyword(s):
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.
2017 ◽
Vol 2017
(725)
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2017 ◽
Vol 147
(3)
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pp. 449-503
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2003 ◽
Vol 2003
(31)
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pp. 2003-2009
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1962 ◽
Vol 13
(3)
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pp. 366-366
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