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From Poincaré to Logarithmic Sobolev Inequalities: A Gradient Flow Approach

✍ Scribed by Dolbeault, Jean; Nazaret, Bruno; Savaré, Giuseppe

Book ID
118119495
Publisher
Society for Industrial and Applied Mathematics
Year
2012
Tongue
English
Weight
366 KB
Volume
44
Category
Article
ISSN
0036-1410

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From super Poincaré to weighted log-Sobo
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✍ Feng-Yu Wang 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 193 KB

We derive weighted log-Sobolev inequalities from a class of super Poincaré inequalities. As an application, Talagrand inequalities with super quadratic cost functions are obtained. In particular, on a complete connected Riemannian manifold, we prove that the log δ -Sobolev inequality with δ ∈ (1, 2)