Two Functionals for which C 1 0 Minimizers are also W 1 o, p Minimizers
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Brezis and Niremberg  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 W1,p0 topology. As an application, we show some existence results involving the sub and super solution method for elliptic equations.
CitationLi, Y., & Xuan, B. (2002). Two functionals for which C 1 0 minimizers are also W 1 o, p minimizers. Electronic Journal of Differential Equations, 2002(09), pp. 1-18.
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