Journal Article10.5802/crmath.161
Sharp rigidity estimates for incompatible fields as a consequence of the Bourgain Brezis div-curl result
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TL;DR: Sharp rigidity estimates and a sharp Korn’s inequality for incompatible fields as a consequence of the Bourgain Brezis div-curl result.
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Abstract: In this note we show that a sharp rigidity estimate and a sharp Korn’s inequality for matrixvalued fields whose incompatibility is a bounded measure can be obtained as a consequence of a Hodge decomposition with critical integrability due to Bourgain and Brezis. Résumé. Dans cette note, nous démontrons qu’une estimée de rigidité et une inégalité de Korn pour des champs avec des valeurs matricielles dont l’incompatibilité est une mesure bornée peuvent être obtenues comme conséquence d’une décomposition de Hodge avec intégrabilité critique dû à Bourgain et Brezis.
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Citations
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L p -trace-free version of the generalized Korn inequality for incompatible tensor fields in arbitrary dimensions
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LawrenceCraig Evans
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TL;DR: In this article, the authors define and define elementary properties of BV functions, including the following: Sobolev Inequalities Compactness Capacity Quasicontinuity Precise Representations of Soboleve Functions Differentiability on Lines BV Function Differentiability and Structure Theorem Approximation and Compactness Traces Extensions Coarea Formula for BV Functions isoperimetric inequalities The Reduced Boundary The Measure Theoretic Boundary Gauss-Green Theorem Pointwise Properties this article.
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A note on div curl inequalities
Loredana Lanzani,Elias M. Stein +1 more
TL;DR: In this article, a scalar smooth function of compact support in R has been shown to fail for all n ≥ 2, where n is the number of vertices in R. The result is reminiscent of the famous inequality of Gagliardo and Nirenberg.
90
Ne\v{c}as-Lions lemma revisited: An $L^p$-version of the generalized Korn inequality for incompatible tensor fields
Peter Lewintan,Patrizio Neff +1 more
TL;DR: In this article, the Poincare inequality was shown to hold for all tensor fields with vanishing tangential trace, and for skew-symmetric tensor field with constant tangential traces.
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On Korn-Maxwell-Sobolev inequalities
Franz Gmeineder,Daniel Spector +1 more
TL;DR: In this article, a family of inequalities that allow one to estimate the L q -norm of a matrix-valued field by the l q −norm of an elliptic part and the l p −norm (i.e., the L p -norm) of the matrixvalued curl was established.