Pseudo-Poincaré Inequalities and Applications to Sobolev Inequalities

  • Laurent Saloff-Coste
Part of the International Mathematical Series book series (IMAT, volume 11)


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.


Riemannian Manifold Sobolev Inequality Isoperimetric Inequality Complete Riemannian Manifold Geodesic Ball 
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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of MathematicsCornell UniversityIthacaUSA

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