Electronic Journal of Differential Equations,
Vol. 1999(1999), No. 38, pp. 1-20.

Title: Boundary behavior and estimates for solutions
       of equations containing the $p$-laplacian

Authors: Jacqueline Fleckinger (Univ. Toulouse-1, Toulouse, France)
         Evans M. Harrell II  (Georgia Tech, Atlanta, GA, USA)
         Francois de Thelin (Univ. Paul Sabatier, Toulouse, France)


Abstract: 
  We use ``Hardy-type'' inequalities to derive $L^q$ 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 $L^q$ 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 $L^q$ 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.