Tilak Bhattacharya
Abstract:
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.
Show me the PDF file (261K), TEX file, and other files for this article.
![]() |
Tilak Bhattacharya Indian Statistical Institute 7, S.J.S. Sansanwal Marg New Delhi 110 016 India e-mail: tlk@isid.isid.ac.in |
Current address:
Mathematics Department, Central Michigan University
Mount Pleasant, MI 48859 USA
e-mail: hadronT@netscape.net