Jacqueline Fleckinger, Evans M. Harrell II,
& Francois de Thelin
Abstract:
We use ``Hardy-type'' inequalities to derive
Lq estimates
for solutions of equations containing the p-Laplacian with p>1.
We begin by deriving some inequalities using elementary ideas
from an early article [B3] which has been largely overlooked.
Then we derive Lq
estimates of the boundary behavior of
test functions of finite energy, and consequently of
principal (positive) eigenfunctions of functionals containing
the p-Laplacian. The estimates contain exponents known to be
sharp when p=2. These lead to estimates of the effect of
boundary perturbation on the fundamental eigenvalue. Finally,
we present global Lq
estimates of solutions of the Cauchy
problem for some initial-value problems containing the
p-Laplacian.
Submitted July 13, 1999. Published September 28, 1999.
Math Subject Classifications: 35J60, 35J70.
Key Words: p-Laplacian, Hardy inequlity,principal eigenvalue,
boundary estimate, boundary perturbation.
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An erratum was attached to this article on April 28, 2003. See the last page to this manuscript.
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Jacqueline Fleckinger CEREMATH & UMR MIP, Universite Toulouse-1 21 allees de Brienne 31000 Toulouse, France e-mail address: jfleck@univ-tlse1.fr |
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Evans M. Harrell II School of Mathematics, Georgia Tech Atlanta, GA 30332-0160, USA, and UMR MIP, Universite Paul Sabatier 31062 Toulouse, France e-mail address: harrell@math.gatech.edu http://www.math.gatech.edu/~harrell/ |
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Francois de Thelin UMR MIP, Universite Paul Sabatier 31062 Toulouse, France e-mail address: dethelin@mip.ups-tlse.fr |
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