Hypoellipticity of the $\bar{\mathrm{\partial }}$-Neumann problem at exponentially degenerate points

We prove that the $\bar{\mathrm{\partial }}$-Neumann solution operator is locally regular in a domain which has compactness estimates, is of finite type outside a curve transversal to the CR directions and for which the holomorphic tangential derivatives of a defining function are subelliptic multipliers in the sense of Kohn.