Bi-Sobolev boundary singularities

Tadeusz Iwaniec; Jani Onninen; Zheng Zhu

doi:10.1007/s40627-023-00114-w

Bi-Sobolev boundary singularities

Tadeusz Iwaniec, Jani Onninen, Zheng Zhu

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Article number	4
Journal	Complex Analysis and its Synergies
Volume	9
Issue number	1
DOIs	https://doi.org/10.1007/s40627-023-00114-w
State	Published - Mar 2023

Keywords

Bi-Sobolev homeomorphisms
Cusp
Quasiball

ASJC Scopus subject areas

Analysis
Mathematics (miscellaneous)
Numerical Analysis

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10.1007/s40627-023-00114-w

Cite this

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title = "Bi-Sobolev boundary singularities",

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{\textquoteright} 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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author = "Tadeusz Iwaniec and Jani Onninen and Zheng Zhu",

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AU - Zhu, Zheng

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AB - 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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KW - Quasiball

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Bi-Sobolev boundary singularities

Abstract

Keywords

ASJC Scopus subject areas

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