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arXiv · 2001.02605

On the existence of extremals for Moser type inequalities in Gauss space

Andrea Cianchi·Vít Musil·Luboš Pick
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Abstract

The existence of an extremal in an exponential Sobolev type inequality, with optimal constant, in Gauss space is established. A key step in the proof is an augmented version of the relevant inequality, which, by contrast, fails for a parallel classical inequality by Moser in the Euclidean space.

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Andrea Cianchi, Vít Musil, Luboš Pick. 2020-01-08. On the existence of extremals for Moser type inequalities in Gauss space. https://doi.org/10.1093/imrn%2Frnaa165

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