Multisummability of formal power series solutions of partial differential equations with constant coefficients

In an earlier paper of the authorʹs, partial differential equations with constant coefficients have been studied. Under a certain (restrictive) assumption upon the equation, those initial conditions were characterized for which the normalized formal solution of a corresponding Cauchy problem is k-summable. Here we treat the general situation and prove an analogous result, using multisummability instead of ksummability. The appropriate multisummability type is shown to depend upon the given PDE only, and can be determined from a corresponding Newton polygon.