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• W2091256209 abstract "We give a sucient condition for the compact embedding from W k;p(¢) 0 (›) to L q(¢) (›) in case essinfx2›(Np(x)=(N i kp(x)) i q(x)) = 0, where › is a bounded open set in R N. As an application, we find a nontrivial nonnegative weak solution of the nonlinear elliptic equation idiv ‡ jru(x)j p(x)i2 ru(x) · = ju(x)j q(x)i2 u(x) in ›, u(x) = 0 on @›. We also consider the existence of a weak solution to the problem above even if the embedding is not compact." @default.
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• W2091256209 date "2010-03-01" @default.
• W2091256209 modified "2023-09-27" @default.
• W2091256209 title "Compact embeddings for Sobolev spaces of variable exponents and existence of solutions for nonlinear elliptic problems involving the p(x)-Laplacian and its critical exponent" @default.
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• W2091256209 doi "https://doi.org/10.5186/aasfm.2010.3507" @default.
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