Pseudo-Poincaré Inequalities and Applications to Sobolev Inequalities

Chapter
Part of the International Mathematical Series book series (IMAT, volume 11)

Abstract

Most smoothing procedures are via averaging. Pseudo-Poincaré inequalities give a basic L p-norm control of such smoothing procedures in terms of the gradient of the function involved. When available, pseudo-Poincaré inequalities are an efficient way to prove Sobolev type inequalities. We review this technique and its applications in various geometric setups.

Keywords

Manifold Nash 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of MathematicsCornell UniversityIthacaUSA

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