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Boundary Conditions and Subelliptic Estimates for Geometric Kramers-Fokker-Planck Operators on Manifolds with Boundaries


About this Title

Francis Nier

Publication: Memoirs of the American Mathematical Society
Publication Year: 2018; Volume 252, Number 1200
ISBNs: 978-1-4704-2802-0 (print); 978-1-4704-4369-6 (online)
DOI: https://doi.org/10.1090/memo/1200
Published electronically: January 23, 2018
Keywords:Kramers-Fokker-Planck equation, Langevin process, hypoelliptic Laplacian, boundary value problem, subelliptic estimates.

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Table of Contents


Chapters

  • Chapter 1. Introduction
  • Chapter 2. One dimensional model problem
  • Chapter 3. Cuspidal semigroups
  • Chapter 4. Separation of variables
  • Chapter 5. General boundary conditions for half-space problems
  • Chapter 6. Geometric Kramers-Fokker-Planck operator
  • Chapter 7. Geometric KFP-operators on manifolds with boundary
  • Chapter 8. Variations on a Theorem
  • Chapter 9. Applications
  • Appendix A. Translation invariant model problems
  • Appendix B. Partitions of unity
  • Acknowledgements

Abstract


This article is concerned with the maximal accretive realizations of geometric Kramers-Fokker-Planck operators on manifolds with boundaries. A general class of boundary conditions is introduced which ensures the maximal accretivity and some global subelliptic estimates. Those estimates imply nice spectral properties as well as exponential decay properties for the associated semigroup. Admissible boundary conditions cover a wide range of applications for the usual scalar Kramer-Fokker-Planck equation or Bismut's hypoelliptic laplacian.

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