Fractional Sobolev Isometric Immersions of Planar Domains
发布时间：2024年04月09日
浏览次数：1102
发布者: He Liu
主讲人： Siran Li(Shanghai Jiao Tong University)
活动时间： 从 2024-04-22 16:00 到 17:00
场地： 智华楼四元厅
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.
