Geodesic
Two functionals for which $C_0^1$ minimizers are also $W_0^{1,p}$ minimizers
Electronic Journal of Differential Equations, Tome 2002 (2002).

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Summary: Brezis and Niremberg [1] showed that for a certain functional the $C_0^1$ minimizer is also the $H_0^1$ minimizer. In this paper, we present two functionals for which a local minimizer in the $C_0^1$ topology is also a local minimizer in the $W_0^{1,p}$ topology. As an application, we show some existence results involving the sub and super solution method for elliptic equations.
Classification : 35J60
Keywords: $W_0^{1$, p$ minimizers$, $C_0^1$ minimizers, divergence elliptic equation, p-Laplacian 
@article{EJDE_2002__2002__a94,
     author = {Li, Yanming and Xuan, Benjin},
     title = {Two functionals for which $C_0^1$ minimizers are also $W_0^{1,p}$ minimizers},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2002},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a94/}
}
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Li, Yanming; Xuan, Benjin. Two functionals for which $C_0^1$ minimizers are also $W_0^{1,p}$ minimizers. Electronic Journal of Differential Equations, Tome 2002 (2002). http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a94/