Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	李思然,上海交通大学
Inviter:
Title:	Fractional Sobolev lsometric lmmersions of Planar Domains
Language:	Chinese
Time & Venue:	2023.06.15 11:00-12:00 南楼N620室
Abstract:	We discuss $C^1$-regularity and developability of isometric immersions of flat domains into $\mathbb{R}^3$ enjoying a local fractional Sobolev $W^{1+s;2s}$-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.