${\ell }^2$ Decoupling in ${\mathbb{R}}^2$ for curves with Vanishing Curvature

Abstract

We expand the class of curves $({\phi }_1(t),{\phi }_2(t)),t\in [0,1]$ for which the ${\ell }^2$ decoupling conjecture holds for $2\le p\le 6$. Our class of curves includes all real-analytic regular curves with isolated points of vanishing curvature and all curves of the form $(t,t^{1+\nu })$ for $\nu \in (0,\infty )$.

11 pages, minor changes, grant information updated