${\mathcal{C}}^m$ solutions of semialgebraic equations on curves

Edward Bierstone, Jean-Baptiste Campesato

Consider a system of equations $A(x)\cdot F(x)=B(x)$ on a subset $X$ of ${\mathbb{R}}^n$, where $A(x)$ and $B(x)$ are matrix- and vector-valued semialgebraic functions on $X$, and t…