On the Spaces Lp(x)(Ω) and Wm, p(x)(Ω)
Xianling Fan,Dun Zhao +1 more
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TLDR
In this paper, the generalized Lebesgue spaces L-p(x)(Omega) and generalized lebesgue-Sobolev spaces W-m,W-p (x) were studied.About:
This article is published in Journal of Mathematical Analysis and Applications.The article was published on 2001-11-15 and is currently open access. It has received 1179 citations till now. The article focuses on the topics: Lp space.read more
Citations
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Eigenvalues of p(x)-Laplacian Dirichlet problem
Xianling Fan,Qihu Zhang,Dun Zhao +2 more
TL;DR: In this paper, the eigenvalues of the p(x)-Laplacian Dirichlet problem were studied and sufficient conditions for infΛ=0 and for inf Λ>0, respectively, were presented.
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Maximal function on Musielak–Orlicz spaces and generalized Lebesgue spaces
TL;DR: In this paper, the Hardy-Littlewood maximal operator M on Musielak-Orlicz Spaces L φ ( R d ) was studied and a necessary condition for the continuity of M on Lφ (R d ) is given.
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A multiplicity result for a nonlinear degenerate problem arising in the theory of electrorheological fluids
TL;DR: In this paper, the boundary value problem is studied and it is shown that if l is large enough then there exist at least two non-negative weak solutions if l > 0.
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On a progress in the theory of lebesgue spaces with variable exponent: maximal and singular operators
TL;DR: The authors presented a broadened version of the plenary lecture presented by the author at the conference Analytic Methods of Analysis and Differential Equations (AMADE-2003), September 4-9, 2003.
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Multiplicity of solutions for p(x) -polyharmonic elliptic Kirchhoff equations
TL;DR: In this article, the existence of an unbounded sequence of solutions for a class of quasilinear elliptic p ( x ) -polyharmonic Kirchhoff equations, including the new delicate degenerate case, was established.
References
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Averaging of functionals of the calculus of variations and elasticity theory
TL;DR: In this paper, the authors developed a duality method in the theory of averaging of nonlinear variational problems with stochastic Lagrangians and derived duality formulas that take account of the regularity problem.
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The quasi-minimizer of integral functionals with m ( x ) growth conditions
Xianling Fan,Dun Zhao +1 more
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The regularity of Lagrangiansf(x, ξ)=254-01254-01254-01with Hölder exponents α(x)
TL;DR: In this paper, the regularity of Lagrangians is studied and the main result is that if α(x) is Holder continuous, then the Lagrangianf(x, ξ)=f (x, ǫ, ε) = |ξ|α(x).