Higher integrability of the gradient in linear elasticity (Q1337515)

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scientific article; zbMATH DE number 683108
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Higher integrability of the gradient in linear elasticity
scientific article; zbMATH DE number 683108

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    Higher integrability of the gradient in linear elasticity (English)
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    9 November 1994
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    The authors investigate higher integrability of the gradient of the solution to a displacement-traction problem that is defined on a bounded \(C^ 1\) domain of \(R^ n\) associated with the linear elasticity equations with \(L^ \infty\) coefficients. This result is established by use of the technique of reverse Hölder inequalities, in which certain interior and boundary estimates are obtained for a local Hardy-Littlewood maximal operator of the gradient. An appropriate interplay between the Sobolev-Poincaré inequality, the Korn inequality and the local geometry of the domain near the interface of the two different boundary conditions plays a major role in establishing these estimates.
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    displacement-traction problem
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    reverse Hölder inequalities
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    local Hardy-Littlewood maximal operator
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    Sobolev-Poincaré inequality
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    Korn inequality
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    local geometry
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