The $p$-Faber-Krahn Inequality Noted

Details The $p$-Faber-Krahn Inequality Noted The $p$-Faber-Krahn Inequality Noted

2009-03-07

arxiv.org/abs/0903.1343v4

Topics Around Research of Vladimir Maz'ya/Internat. Math. Series, Springer, Vol. 11-13, 2009

Mathematics

Analysis of PDEs

Scientific paper

When revisiting the Faber-Krahn inequality for the principal $p$-Laplacian eigenvalue of a bounded open set in $\mathbb R^n$ 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.

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