Inhomogeneous symbols, the Newton polygon, and maximal L_p-regularity

We prove a maximal regularity result for operators corresponding to rotation invariant (in space) symbols which are inhomogeneous in space and time. Symbols of this type frequently arise in the treatment of half-space models for (free) boundary value problems. The result is obtained by extending the Newton polygon approach to variables living in complex sectors and combining it with abstract results on H_\infty-calculus and R-bounded operator families. As an application we derive maximal regularity for the linearized Stefan problem with Gibbs-Thomson correction.