W1,p versus C1 local minimizers and multiplicity results for quasilinear elliptic equations

In this paper we show that the local minimizers of a class of functionals in the C1-topology are still their local minimizers in W 1,p 0 (Ω). Using this fact, we study the multiplicity of solutions for a class of quasilinear elliptic equations via critical point theory.  2003 Elsevier Inc. All rights reserved