Sobolev Trace Inequalities

Details Sobolev Trace Inequalities Sobolev Trace Inequalities

2001-07-09

arxiv.org/abs/math/0107065v1

Mathematics

Classical Analysis and ODEs

16 pages

Scientific paper

The existence of extremal functions for the Sobolev trace inequalities is studied using the concentration compactness theorem. The conjectured extremal, the function of conformal factor, is considered and is proved to be an actual extremal function with extra symmetry condition on functions. One of the limiting cases of the Sobolev trace inequalities is investigated and the best constant for this case is computed.

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