A Korn-type inequality in SBD for functions with small jump sets

Friedrich M (2017)

Publication Type: Journal article

Publication year: 2017

Journal

Mathematical Models & Methods in Applied Sciences World Scientific Publishing

Book Volume: 27

Pages Range: 2461-2484

Journal Issue: 13

DOI: 10.1142/S021820251750049X

Abstract

We present a Korn-type inequality in a planar setting for special functions of bounded deformation. We prove that for each function in SBD2 with a sufficiently small jump set the distance of the function and its derivative from an infinitesimal rigid motion can be controlled in terms of the linearized elastic strain outside of a small exceptional set of finite perimeter. Particularly, the result shows that each function in SBD2 has bounded variation away from an arbitrarily small part of the domain.

Authors with CRIS profile

Manuel Friedrich

Involved external institutions

Universität Wien / University of Vienna AT Austria (AT)

How to cite

APA:

Friedrich, M. (2017). A Korn-type inequality in SBD for functions with small jump sets. Mathematical Models & Methods in Applied Sciences, 27(13), 2461-2484. https://doi.org/10.1142/S021820251750049X

MLA:

Friedrich, Manuel. "A Korn-type inequality in SBD for functions with small jump sets." Mathematical Models & Methods in Applied Sciences 27.13 (2017): 2461-2484.

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