A Necessary and Sufficient Condition for the Existence of Absolute Minimizers for Energy Functionals with Scale Invariance


In (Haidar 2009) and (Haidar 2007), we constructed models in higher dimensional nonlinear hyper-elasticity that establish that strong ellipticity of the stored energy does not imply that all solutions to the corresponding equilibrium equations which pass through the origin and have finite energy are trivial. While that work, by itself, settled a longstanding problem posed by J. Ball in 1982 (Ball 1982), it also shed new light on another central, very difficult problem of nonlinear elasticity, namely, that of regularity of weak equilibria and material instabilities.


Lagrange Equation Nonlinear Partial Differential Equation Absolute Minimizer Nonlinear Elasticity Energy Functional 
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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Grand Valley State UniversityAllendaleUSA

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