Browsing by Author "Mora-Corral, Carlos"

Now showing 1 - 3 of 3
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    Global invertibility of Sobolev maps
    (2021) Henao, Duvan; Mora-Corral, Carlos; Oliva, Marcos
    We define a class of Sobolev W1-p(Omega, R-n) functions, with p > n -1, such that its trace on de is also Sobolev, and do not present cavitation in the interior or on the boundary. We show that if a function in this class has positive Jacobian and coincides on the boundary with an injective map, then the function is itself injective. We then prove the existence of minimizers within this class for the type of functionals that appear in nonlinear elasticity.
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    Harmonic Dipoles and the Relaxation of the Neo-Hookean Energy in 3D Elasticity
    (2023) Barchiesi, Marco; Henao, Duvan; Mora-Corral, Carlos; Rodiac, Remy
    We consider the problem of minimizing the neo-Hookean energy in 3D. The difficulty of this problem is that the space of maps without cavitation is not compact, as shown by Conti & De Lellis with a pathological example involving a dipole. In order to rule out this behaviour we consider the relaxation of the neo-Hookean energy in the space of axisymmetric maps without cavitation. We propose a minimization space and a new explicit energy penalizing the creation of dipoles. This new energy, which is a lower bound of the relaxation of the original energy, bears strong similarities with the relaxed energy of Bethuel-Brezis-Helein in the context of harmonic maps into the sphere.
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    On the lack of compactness in the axisymmetric neo-Hookean model
    (2024) Barchiesi, Marco; Henao, Duvan; Mora-Corral, Carlos; Rodiac, Remy
    We provide a fine description of the weak limit of sequences of regular axisymmetric maps with equibounded neo-Hookean energy, under the assumption that they have finite surface energy. We prove that these weak limits have a dipole structure, showing that the singular map described by Conti and De Lellis is generic in some sense. On this map, we provide the explicit relaxation of the neo-Hookean energy. We also make a link with Cartesian currents showing that the candidate for the relaxation we obtained presents strong similarities with the relaxed energy in the context of $\mathbb {S}<^>2$ -valued harmonic maps.