Summary
In this paper we introduce some new classes of functions, among these a class of weak diffeomorphisms. In these classes we prove by direct methods the existence of minimizers for several kinds of variational integrals. In particular, we prove the existence of one-to-one orientation-preserving maps that minimize suitable energies associated with hyperelastic materials. The minimizers are also proved to satisfy equilibrium equations. Finally radial deformations are discussed in connection with cavitation.
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Communicated by E. Giusti & S. Antman
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Giaquinta, M., Modica, G. & souček, J. Cartesian currents, weak diffeomorphisms and existence theorems in nonlinear elasticity. Arch. Rational Mech. Anal. 106, 97–159 (1989). https://doi.org/10.1007/BF00251429
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DOI: https://doi.org/10.1007/BF00251429