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

Andrea Cianchi

doi:10.1017/S0308210511000758

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.

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

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This article has been cited by the following publications. This list is generated based on data provided by Crossref.

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

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