November 1, 2001Open Access

On the Spaces Lp(x)(Ω) and Wm,p(x)(Ω)

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In this paper we present some basic results on the generalized Lebesgue spaces L-p(x)(Omega) and generalized Lebesgue-Sobolev spaces W-m,W-p(x)(Omega). These results provide the necessary framework for the study of variational problems and elliptic equations with non-standard p(x)-growth conditions. (C) 2001 Academic Press.

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Xianling Fan

Shaanxi University of Chinese Medicine

Dun Zhao

Lanzhou University of Finance and Economics

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Journal of Mathematical Analysis and Applications

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Lanzhou University

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Fan et al. (Thu,) studied this question.

synapsesocial.com/papers/697b2442e73565ae06777aa2 — DOI: https://doi.org/10.1006/jmaa.2000.7617

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AVERAGING OF FUNCTIONALS OF THE CALCULUS OF VARIATIONS AND ELASTICITY THEORY· 1987 · 1,274 citations

Also consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

The quasi-minimizer of integral functionals with m(x) growth conditions· 2000 · 76 citations
Variational Methods for the Study of Nonlinear Operators· 1966 · 842 citations
The regularity of Lagrangiansf(x, ξ)=254-01254-01254-01with Hölder exponents α(x)· 1996 · 26 citations
Orlicz Spaces and Modular Spaces· 1983 · 2,008 citations
AVERAGING OF FUNCTIONALS OF THE CALCULUS OF VARIATIONS AND ELASTICITY THEORY· 1987 · 1,274 citations

On the Spaces Lp(x)(Ω) and Wm,p(x)(Ω)

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