TY - JOUR
T1 - Korn's inequalities
T2 - The linear vs. the nonlinear case
AU - Ciarlet, Philippe G.
PY - 2012/6
Y1 - 2012/6
N2 - It is well known that the linear Korn inequality pervades the theory of three-dimensional linearized elasticity. It is thus conceivable that nonlinear Korn's inequalities could likewise play a role in the theory of three-dimensional nonlinear elasticity. In this paper, we describe the (available to this date) linear and nonlinear Korn's inequalities and we discuss the resemblances, but also the sometimes intriguing di erences, that exist between these two kinds of inequalities.
AB - It is well known that the linear Korn inequality pervades the theory of three-dimensional linearized elasticity. It is thus conceivable that nonlinear Korn's inequalities could likewise play a role in the theory of three-dimensional nonlinear elasticity. In this paper, we describe the (available to this date) linear and nonlinear Korn's inequalities and we discuss the resemblances, but also the sometimes intriguing di erences, that exist between these two kinds of inequalities.
KW - Dimension theory
KW - Multifractal analysis
KW - Poincaré recurrences
UR - http://www.scopus.com/inward/record.url?scp=84864481050&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84864481050&origin=recordpage
U2 - 10.3934/dcdss.2012.5.473
DO - 10.3934/dcdss.2012.5.473
M3 - RGC 21 - Publication in refereed journal
SN - 1937-1632
VL - 5
SP - 473
EP - 483
JO - Discrete and Continuous Dynamical Systems - Series S
JF - Discrete and Continuous Dynamical Systems - Series S
IS - 3
ER -