Editing Riemann mapping theorem (section)

==Smooth Riemann mapping theorem==
In the case of a simply connected bounded domain with smooth boundary, the Riemann mapping function and all its derivatives extend by continuity to the closure of the domain. This can be proved using regularity properties of solutions of the Dirichlet boundary value problem, which follow either from the theory of [[Sobolev spaces for planar domains#Application to smooth Riemann mapping theorem|Sobolev spaces for planar domains]] or from [[Neumann–Poincaré operator#Solution of Dirichlet and Neumann problems|classical potential theory]]. Other methods for proving the smooth Riemann mapping theorem include the theory of kernel functions<ref>{{harvnb|Bell|1992}}</ref> or the [[Beltrami equation#Smooth Riemann mapping theorem|Beltrami equation]].