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On the Spaces L and W
Xianling Fan,Dun Zhao +1 more
- 01 Jan 2001
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About: The article was published on 01 Jan 2001. and is currently open access.
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Citations
The variable exponent Sobolev capacity and quasi-fine properties of Sobolev functions in the case p−=1
Heikki Hakkarainen,Matti Nuortio +1 more
TL;DR: In this paper, it was shown that the variable exponent Sobolev capacity is subadditive for variable exponents satisfying 1 ⩽ p ∞ and that if the exponent is log-Holder continuous, then the functions of the function have Lebesgue points quasieverywhere and they have quasicontinuous representatives also in the case p − = 1.
4
Solutions for a class of hemivariational inequalities with p(x)-Laplacian
Xia Zhang,Yongqiang Fu +1 more
TL;DR: In this paper, a class of hemivariational inequalities with p(x)-Laplacian is studied and the existence of solutions on interior and exterior domains is obtained by applying nonsmooth critical point theory for locally Lipschitz functions.
A Gamma convergence approach to the critical Sobolev embedding in variable exponent spaces
TL;DR: In this article, the critical Sobolev embeddings W 1, p ( ⋅ ) ( Ω ) ⊂ L p ⁎ (⋅ ǫ ) (Ω ) ( ) for variable exponent Soboleve spaces were studied from the point of view of the Γ-convergence and a sufficient condition for the existence of extremals for the best constant was provided.
4
Three solutions for a class of quasilinear elliptic systems involving the p(x)-Laplace operator
Honghui Yin,Zuodong Yang +1 more
TL;DR: In this article, the existence of at least three weak solutions for quasilinear elliptic systems involving the p(x)-Laplace operator with Neumann boundary condition is established.
On a nonlocal problem involving the fractional \begin{document}$ p(x,.) $\end{document} -Laplacian satisfying Cerami condition
Elhoussine Azroul,Abdelmoujib Benkirane,and Mohammed Shimi +2 more
- 01 Jan 2021
TL;DR: In this paper, the existence and multiplicity of solutions for a class of fractional Laplacian problems with the nonlocal Dirichlet boundary data was investigated, where the nonlinearity is superlinear but does not satisfy the usual Ambrosetti-Rabinowitz condition.
4
References
•Book
Orlicz Spaces and Modular Spaces
Julian Musielak
- 01 Nov 1983
TL;DR: In this paper, a family of modulars depending on a parameter is described, and some applications of modular spaces are discussed, including orlicz spaces and countably modulared spaces.
2.1K
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.
1.3K