Dev-Div- and DevSym-DevCurl-inequalities for incompatible square tensor fields with mixed boundary conditions
Analysis of PDEs
2013-07-05 v1 Functional Analysis
Numerical Analysis
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.
Cite
@article{arxiv.1307.1434,
title = {Dev-Div- and DevSym-DevCurl-inequalities for incompatible square tensor fields with mixed boundary conditions},
author = {Sebastian Bauer and Patrizio Neff and Dirk Pauly and Gerhard Starke},
journal= {arXiv preprint arXiv:1307.1434},
year = {2013}
}
Comments
19 pages