Abstract
We present a simple direct proof of the classical Sobolev inequality in \(\mathbb{R}^n\) with best constant from the geometric Brunn–Minkowski–Lusternik inequality.
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Research supported in part by NSF Gr. No. 0405587 and B. Zegarlinski’s Pierre de Fermat Grant 2006 from the Région Midi-Pyrénées, France.
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Bobkov, S.G., Ledoux, M. From Brunn–Minkowski to sharp Sobolev inequalities. Annali di Matematica 187, 369–384 (2008). https://doi.org/10.1007/s10231-007-0047-0
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DOI: https://doi.org/10.1007/s10231-007-0047-0