Holomorphic dependence for the Beltrami equation in Sobolev spaces

Christian El Emam, Nathaniel Sagman

We prove that, given a path of Beltrami differentials on $\mathbb{C}$ that live in and vary holomorphically in the Sobolev space $W_{loc}^{l,\infty }(\hat{I}\text{c◯})$ of an open subset $Ω\subse…