A problem of minimization with relaxed energy

Rejeb Hadiji; Feng Zhou

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Remarks on the theory of elasticity

Sergio Conti, Camillo de Lellis (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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In compressible Neohookean elasticity one minimizes functionals which are composed by the sum of the $L^{2}$ norm of the deformation gradient and a nonlinear function of the determinant of the gradient. Non–interpenetrability of matter is then represented by additional invertibility conditions. An existence theory which includes a precise notion of invertibility and allows for cavitation was formulated by Müller and Spector in 1995. It applies, however, only if some $L^{p}$ -norm of the gradient...