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- W4381609919 abstract "We discuss $C^1$ regularity and developability of isometric immersions of flat domains into $mathbb R^3$ enjoying a local fractional Sobolev $W^{1+s, frac2s}$ regularity for $2/3 le s< 1 $, generalizing the known results on Sobolev and Holder regimes. Ingredients of the proof include analysis of the weak Codazzi-Mainardi equations of the isometric immersions and study of $W^{2,frac2s}$ planar deformations with symmetric Jacobian derivative and vanishing distributional Jacobian determinant. On the way, we also show that the distributional Jacobian determinant, conceived as an operator defined on the Jacobian matrix, behaves like determinant of gradient matrices under products by scalar functions." @default.
- W4381609919 created "2023-06-23" @default.
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- W4381609919 date "2021-03-02" @default.
- W4381609919 modified "2023-09-25" @default.
- W4381609919 title "Fractional Sobolev isometric immersions of planar domains" @default.
- W4381609919 doi "https://doi.org/10.48550/arxiv.2103.01723" @default.
- W4381609919 hasPublicationYear "2021" @default.
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