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

S. M. Haidar ()
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S. M. Haidar: Grand Valley State University

A chapter in Integral Methods in Science and Engineering, 2011, pp 181-190 from Springer

Abstract: Abstract 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.

Keywords: Lagrange Equation; Nonlinear Partial Differential Equation; Absolute Minimizer; Nonlinear Elasticity; Energy Functional (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-8176-8238-5_17

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DOI: 10.1007/978-0-8176-8238-5_17

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