Two Functionals for which C 1 0 Minimizers are also W 1 o, p Minimizers

Abstract

Brezis and Niremberg [1] showed that for a certain functional the C¹₀ minimizer is also the H¹₀ minimizer. In this paper, we present two functionals for which a local minimizer in the C¹₀ topology is also a local minimizer in the W¹₀,p topology. As an application, we show some existence results involving the sub and super solution method for elliptic equations.