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sobolev–slobodeckiĭ

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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Nonlinear elasticity with vanishing nonlocal self-repulsion
Part of
- Miscellaneous topics in calculus of variations and optimal control
- Equations of mathematical physics and other areas of application
Stefan Krömer, Philipp Reiter
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Proceedings of the Royal Society of Edinburgh. Section A: Mathematics , First View

Published online by Cambridge University Press:

28 September 2023, pp. 1-18
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We prove that for nonlinear elastic energies with strong enough energetic control of the outer distortion of admissible deformations, almost everywhere global invertibility as constraint can be obtained in the $\Gamma$-limit of the elastic energy with an added nonlocal self-repulsion term with asymptocially vanishing coefficient. The self-repulsion term considered here formally coincides with a Sobolev–Slobodeckiĭ seminorm of the inverse deformation. Variants near the boundary or on the surface of the domain are also studied.