The p-Faber-Krahn Inequality Noted

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


When revisiting the Faber-Krahn inequality for the principal p- Laplacian eigenvalue of a bounded open set in R n with smooth boundary, we simply rename it as the p-Faber-Krahn inequality and interestingly find that this inequality may be improved but also characterized through Maz'ya's capacity method, the Euclidean volume, the Sobolev type inequality and Moser-Trudinger's inequality.


Sobolev Inequality Isoperimetric Inequality Euclidean Ball Laplacian Eigenvalue Nonnegative Ricci Curvature 
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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsMemorial University of NewfoundlandSt. John’sCanada

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