Speaker: Siran Li (Shanghai Jiao Tong University)
Time: 15:00-16:00, Jun 7, 2023
Room: Tencent Meeting ID: 679 730 042, no password & room 414, Building 2, Shanghai Institute for Advanced Studies, USTC
We discuss $C^1$-regularity and developability of isometric immersions of flat domains into $\mathbb{R}^3$ enjoying a local fractional Sobolev $W^{1+s;2/s}$-regularity for $2/3 \leq s < 1$, generalizing the known results on Sobolev and H\{o}lder regimes. Ingredients of the proof include analysis of the weak Codazzi equations of the isometric immersions and study of $W^{1+s;2/s}$-gradient 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. Joint work with Reza Pakzad and Armin Schikorra.
