(untitled) (Contemporary Mathematics, 2022)
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.