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

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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.

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Acknowledgment

This work was supported by JSPS KAKENHI Grant Number JP20K03679.

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Authors and Affiliations

  1. Department of Mathematics, Osaka University, Oyonaka, Osaka, 560-0043, Japan

    Tatsuo Nishitani

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  1. Tatsuo Nishitani
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Nishitani, T. The Cauchy problem for operators with triple effectively hyperbolic characteristics: Ivrii’s conjecture. JAMA 149, 167–237 (2023). https://doi.org/10.1007/s11854-022-0249-9

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  • DOI: https://doi.org/10.1007/s11854-022-0249-9

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