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Sharp Global Bounds for the Hessian on Pseudo-Hermitian Manifolds

  • Sagun ChanilloEmail author
  • Juan J. Manfredi
Chapter
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

We consider an abstract CR manifold equipped with a strictly positive definite Levi form, which defines a pseudo-Hermitian metric on the manifold. On such a manifold it is possible to define a natural sums of squares sub-Laplacian operator. We use Bochner identities to obtain Cordes–Friedrichs type inequalities on such manifolds where the L 2 norm of the Hessian tensor of a function is controlled by the L 2 norm of the sub-Laplacian of the function with a sharp constant for the inequality. By perturbation we proceed to develop a Cordes–Nirenberg type theory for non-divergence form equations on CR manifolds. Some applications are given to the regularity of p-Laplacians on CR manifolds.

Keywords

Heisenberg Group Levi Form Paneitz Operator Cordes Condition Hessian Tensor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Boston 2010

Authors and Affiliations

  1. 1.Rutgers UniversityPiscatawayUSA
  2. 2.Department of MathematicsUniversity of PittsburghPittsburghUSA

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