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A strong maximum principle for globally hypoelliptic operators

  • Kazuaki TairaEmail author
Article
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Abstract

In this paper we study the strong maximum principle for globally hypoelliptic differential operators of second-order, and reveal the underlying analytical mechanism of propagation of maximums in terms of the Lie algebra generated by diffusion vector fields and the Fichera function. Our formulation of the strong maximum principle is coordinate-free. The results here may be applied to questions of uniqueness for degenerate elliptic boundary value problems on a manifold. Furthermore, the mechanism of propagation of maximums plays an important role in the interpretation and study of Markov processes from the viewpoint of functional analysis.

Keywords

Globally hypoelliptic operator Strong maximum principle Lie algebra Fichera function 

Mathematics Subject Classification

35J70 35H10 58G20 35K65 

Notes

Acknowledgements

The author is grateful to the referee for many valuable suggestions and comments, which have improved substantially the presentation of the present paper. He is also indebted to Professors Hajime Sato and Koichi Uchiyama for formulating the mapping \(\varPsi \) in terms of differential geometry.

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Copyright information

© Springer-Verlag Italia S.r.l., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of TsukubaTsukubaJapan

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