科研之友
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摘要
The best constant in a mean-value trace inequality for functions of bounded variation on admissible domains Omega subset of R-n is shown to agree with an isoperimetric constant associated with Omega. The existence and form of extremals is also discussed. This result is exploited to compute the best constant in the relevant trace inequality when Omega 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 Omega is a disc in R-2.
- 出版日期2012-12
