Strong unique continuation for systems of complex vector fields

Abstract

In this work we study the property of strong unique continuation, at a given point, for Gevrey solutions to homogeneous systems of PDE defined by complex, real-analytic vector fields in involution. We show that when the system is minimal at the point then the strong unique continuation property holds for Gevrey solutions of order σ∈[1,2] and, furthermore, when the minimality property fails to hold then there are non-trivial Gevrey flat solutions of any given order σ>1. The case of Gevrey order σ>2 is also studied for some particular classes of involutive systems.