A Lavrentiev phenomenon in the neo-Hookean model
Abstract
We exhibit a Lavrentiev gap phenomenon for the neo-Hookean energy in three-dimensional nonlinear elasticity. More precisely, we construct boundary data for which the infimum of the neo-Hookean energy over deformations satisfying a natural regularity and invertibility condition is strictly larger than the infimum over the weak H1-closure of that class. The mechanism underlying the gap is a deformation with a dipole-type singularity.
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