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Annali di Matematica Pura ed Applicata

, Volume 177, Issue 1, pp 225–240 | Cite as

A proof of the Faber-Krahn inequality for the first eigenvalue of thep-Laplacian

  • Tilak Bhattacharya
Article

Summary

In this work we present an elementary proof of the Faber-Krahn inequality for the first eigenvalue of the p-Laplacian on bounded domains in ℝn. Let λ1 be the first eigenvalue and λ 1 * be the first eigenvalue for the ball of the same volume. Then we show that λ1 1 * iff the domain is a ball. Our proof makes considerable use of the corresponding Talenti's inequality and some well known properties of the first eigenfunction.

Keywords

Elliptic Equation Maximal Function Measure Zero Orlicz Space Isoperimetric Inequality 
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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1999

Authors and Affiliations

  • Tilak Bhattacharya
    • 1
  1. 1.Indian Statistical InstituteNew DelhiIndia

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