A Decomposition Lemma in Convex Integration via Classical Algebraic Geometry

Zhitong Su, Weijun Zhang

In this paper, we prove a decomposition lemma for symmetric matrix fields on bounded domains: $D+\mathrm{Sym}\nabla \Phi ={\sum }_i{a}_i^2{\xi }_i\otimes {\xi }_i$ with uniform control on $\Phi$ and $a_i…