Electron. J. Diff. Eqns., Vol. 2002(2002), No. 09, pp. 1-18.

Two functionals for which $C_0^1$ minimizers are also $W_0^{1,p}$ minimizers

Yanming Li & Benjin Xuan

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.

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  Yanming Li
Department of SCGY
University of Science and Technology of China
Hefei, Anhui 230026, China
e-mail: lyqg@mail.ustc.edu.cn
Benjin Xuan
Department of Mathematics
University of Science and Technology of China
Dept. de Matematicas, Universidad Nacional
Bogota, Colombia
e-mail: wenyuanxbj@yahoo.com

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