<f>W1,p</f> versus <f>C1</f> 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 <f>C1</f>-topology are still their local minimizers in <f>W1,p0(Ω)</f>. Using this fact, we study the multiplicity of solutions for a class of quasilinear elliptic equations via critical point theory. [Copyright &y& Elsevier]