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arXiv · 1307.1434

Dev-Div- and DevSym-DevCurl-inequalities for incompatible square tensor fields with mixed boundary conditions

Sebastian Bauer·Patrizio Neff·Dirk Pauly·Gerhard Starke
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Abstract

For an n-dimensional bounded domain we derive some inequalities bounding the norm of a square tensor field. Concerning the Div-Dev-inequality the bound is given by the trace-free part and the divergence and the tensor. In the case of the DevSym-Curl-inequality the bound is given by the trace-free and symmetric part and the curl of the tensor. For n=3 the bound is given by the trace-free symmetric part of the tensor and the trace-free part of the curl of the tensor. Some prototype applications are presented in which the new inequalities may be used to derive the coercivity of the models.

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Sebastian Bauer, Patrizio Neff, Dirk Pauly, Gerhard Starke. 2013-07-04. Dev-Div- and DevSym-DevCurl-inequalities for incompatible square tensor fields with mixed boundary conditions. https://arxiv.org/abs/1307.1434

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