Global integrability of the Jacobian of a composite mapping.
Ding, Shusen, Liu, Bing (2006)
Journal of Inequalities and Applications [electronic only]
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Ding, Shusen, Liu, Bing (2006)
Journal of Inequalities and Applications [electronic only]
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Yongqiang Fu, Binlin Zhang (2013)
Czechoslovak Mathematical Journal
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In this paper we consider the following Dirichlet problem for elliptic systems: where is a Dirac operator in Euclidean space, is defined in a bounded Lipschitz domain in and takes value in Clifford algebras. We first introduce variable exponent Sobolev spaces of Clifford-valued functions, then discuss the properties of these spaces and the related operator theory in these spaces. Using the Galerkin method, we obtain the existence of weak solutions to the scalar part of the...
Wang, Yong, Li, Guanfeng (2010)
Journal of Inequalities and Applications [electronic only]
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Asif, Muhammad, Meskhi, Alexander (2008)
Journal of Inequalities and Applications [electronic only]
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Jingshi Xu (2007)
Czechoslovak Mathematical Journal
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The boundednees of multilinear commutators of Calderón-Zygmund singular integrals on Lebesgue spaces with variable exponent is obtained. The multilinear commutators of generalized Hardy-Littlewood maximal operator are also considered.
Cesare Davini, Roberto Paroni (2008)
ESAIM: Control, Optimisation and Calculus of Variations
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Here we present an approximation method for a rather broad class of first order variational problems in spaces of piece-wise constant functions over triangulations of the base domain. The convergence of the method is based on an inequality involving norms obtained by Nečas and on the general framework of -convergence theory.