Geodesic
Two functionals for which \(C_0^1\) minimizers are also \(W_0^{1,p}\) minimizers
Electronic journal of differential equations, Tome 2002 (2002)
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__a294,
     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},
     year = {2002},
     volume = {2002},
     zbl = {1103.35317},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a294/}
}
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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__a294/