Electronic Journal of Differential Equations,
Vol. 2002(2002), No. 09, pp. 1-18.

Title: Two functionals for which $C^1_0$ minimizers are also
       $W_0^{1,p}$ minimizers
   
Authors:  Yanming Li (Univ. o Science & Tech., Hefei, China)
          Benjin Xuan (Univ. Nacional, Bogota, Colombia)

Abstract:  
  Brezis and Niremberg [1] showed that for a certain
  functional the $C_0^1$ minimizer is also the $H_0^1$ minimizer.
  In this paper, we present two functionals for which
  a local minimizer in the  $C_0^1$ topology is also a local
  minimizer in the  $W_0^{1,p}$ topology.
  As an application, we show some existence results involving 
  the sub and super solution method for elliptic equations.
  
Submitted November 24, 2001. Published January 24, 2002.
Math Subject Classifications: 35J60.
Key Words: $W_0^{1;p}$ minimizers; $C_0^1$ minimizers; 
divergence elliptic equation; p-Laplacian.