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.