Propagation of Singularities in the Ramified Cauchy Problem for a Class of Operators with Non-involutive Multiple Characteristics

Abstract

In the ramified Cauchy problem, analytic continuation of holomorphic solutions has been mainly studied. In this paper, we prove the propagation of singularities for a class of linear partial differential equations with non-involutive multiple characteristics. §1. IntroductionIn this paper, we consider the Cauchy problem in a complex domain with singular initial data and study the propagation of singularities of the solution.It is one of the most fundamental problems in the theory of partial differential equations, and its study goes back to J. Leray