Fractional Sobolev Isometric Immersions of Planar Domains
Time: 2024-04-09
Published By: He Liu
Speaker(s): Siran Li(Shanghai Jiao Tong University)
Time: 16:00-17:00 April 22, 2024
Venue: Siyuan Lecture Hall, Zhihua Building
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 $2/3 \leq s < 1$, generalising the known results on Sobolev (by Pakzad) and H\"{o}lder (by De Lellis--Pakzad) regimes. Ingredients of the proof include analysis of the weak Codazzi equations of isometric immersions, the study of $W^{1+s;2/s}$-gradient deformations with symmetric derivative and vanishing distributional Jacobian determinant, and the theory of compensated compactness. Joint work with M. Reza Pakzad and Armin Schikorra.
