The Cauchy problem for operators with triple effectively hyperbolic characteristics: Ivrii’s conjecture

Abstract

Ivrii’s conjecture asserts that the Cauchy problem is C∞ well-posed for any lower order term if every singular point of the characteristic variety is effectively hyperbolic. An effectively hyperbolic singular point is at most a triple characteristic. If every characteristic is at most double, this conjecture has been proved in the 1980’s. In this paper we prove the conjecture for the remaining cases, that is for operators with triple effectively hyperbolic characteristics.