C¹(Rᴺ) Versus W¹,ᵖ(Rᴺ) Local Minimizers
Keywords:quasilinear elliptic equation in Rᴺ, p-Laplacian, energy functional, local minimizer, Sobolev spaces
This paper deals with the energy functional associated with a quasilinear elliptic equation in RN which is driven by the p-Laplacian operator. It is shown for such functional that any C1(RN) local minimizer in an appropriate sense is a W1,p(RN) local minimizer. This extends to RN the celebrated property of Brezis-Nirenberg type known for bounded domains.