Resumen de Remarks on the theory of elasticity
Sergio Conti, Camillo de Lellis
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 with p>2 is controlled (in three dimensions). We first characterize their class of functions in terms of properties of the associated rectifiable current. Then we address the physically relevant p=2 case, and show how their notion of invertibility can be extended to p=2. The class of functions so obtained is, however, not closed. We prove this by giving an explicit construction.
