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- Q3154002 subject Q7213511.
- Q3154002 subject Q7464113.
- Q3154002 subject Q8756019.
- Q3154002 abstract "In mathematical analysis, Korn's inequality is an inequality concerning the gradient of a vector field that generalizes the following classical theorem: if the gradient of a vector field is skew-symmetric at every point, then the gradient must be equal to a constant skew-symmetric matrix. Korn's theorem is a quantitative version of this statement, which intuitively says that if the gradient of a vector field is on average not far from the space of skew-symmetric matrices, then the gradient must not be far from a particular skew-symmetric matrix. The statement that Korn's inequality generalizes thus arises as a special case of rigidity.In (linear) elasticity theory, the symmetric part of the gradient is a measure of the strain that an elastic body experiences when it is deformed by a given vector-valued function. The inequality is therefore an important tool as an a priori estimate in linear elasticity theory.".
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- Q3154002 wikiPageWikiLink Q7213511.
- Q3154002 wikiPageWikiLink Q7464113.
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- Q3154002 wikiPageWikiLink Q8756019.
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- Q3154002 wikiPageWikiLink Q956437.
- Q3154002 comment "In mathematical analysis, Korn's inequality is an inequality concerning the gradient of a vector field that generalizes the following classical theorem: if the gradient of a vector field is skew-symmetric at every point, then the gradient must be equal to a constant skew-symmetric matrix.".
- Q3154002 label "Korn's inequality".