Korn's First Inequality with variable coefficients and its generalization
Waldemar Pompe (2003)
Commentationes Mathematicae Universitatis Carolinae
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If is a bounded domain with Lipschitz boundary and is an open subset of , we prove that the following inequality holds for all and , where defines an elliptic differential operator of first order with continuous coefficients on . As a special case we obtain for all vanishing on , where is a continuous mapping with . Next we show that is not valid if , and , but does hold if , and is symmetric and positive definite in .