In this work, we present a lower bound for the first eigenvalue of the p-Laplacian on bounded domains in . Let be the first eigenvalue and be the first eigenvalue for the ball of the same volume. Then we show that , for some constant , where is the asymmetry of the domain . This provides a lower bound sharper than the bound in Faber-Krahn inequality.
Submitted September 3, 2000. Published May 16, 2001.
Math Subject Classifications: 35J60, 35P30.
Key Words: Asymmetry, De Giorgi perimeter, p-Laplacian, first eigenvalue, Talenti's inequality.
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|Tilak Bhattacharya |
Indian Statistical Institute
7, S.J.S. Sansanwal Marg
New Delhi 110 016 India
Mathematics Department, Central Michigan University
Mount Pleasant, MI 48859 USA