Abstract
We provide sharp geometric descriptions of boundary singularities in the form of cusps that can be created by a deformation of a hyperelastic body which stores a given bi-Sobolev type energy. Guided by Hookes’ Law, we investigate when the deformed configuration returns to its original shape by applying the inverse deformation with the same finite energy.
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Acknowledgements
T. Iwaniec was supported by the NSF Grant DMS-1802107. J. Onninen was supported by the NSF Grant DMS-1700274. Z. Zhu was support by the Academy of Finland via the Centre of Excellence in Analysis and Dynamics Research (project No. 271983) and the CSC Grant CSC201506020103 from China.
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Dedicated to Pekka Koskela on the occasion of his 60th birthday.
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Iwaniec, T., Onninen, J. & Zhu, Z. Bi-Sobolev boundary singularities. Complex Anal Synerg 9, 4 (2023). https://doi.org/10.1007/s40627-023-00114-w
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DOI: https://doi.org/10.1007/s40627-023-00114-w