Balls have the worst best Sobolev inequalities. II: Variants and extensions
This is the sequel to [J.~Geom. Anal. 15, No. 1, 83--121 (2005; Zbl 1086.46021)] about the derivation of sharp Sobolev type inequalities in \({\mathbb R}^n\) by means of mass transport methods. The goal of the present paper is to consider three different kinds of extensions of previous results: (1) with trace term in Lipschitz domains, (2) limit inequalities such as trace Faber-Krahn inequalities, trace \(L^p\)-logarithmic Sobolev inequalities and trace Moser-Trudinger inequalities, (3) inequalities on angular domains for which the trace term disappears.
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