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

Abstract

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 functional calculus and R-bounded operator families. As an application we derive maximal regularity for the linearized Stefan problem with Gibbs-Thomson correction.