Sharp Global Bounds for the Hessian on Pseudo-Hermitian Manifolds

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We find sharp bounds for the norm inequality on a Pseudo-hermitian manifold, where the L^2 norm of all second derivatives of the function involving horizontal derivatives is controlled by the L^2 norm of the sub-Laplacian. Perturbation allows us to get a-priori bounds for solutions to sub-elliptic PDE in non-divergence form with bounded measurable coefficients. The method of proof is through a Bochner technique. The Heisenberg group is seen to be en extremal manifold for our inequality in the class of manifolds whose Ricci curvature is non-negative.
13 pages

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Analysis of PDEs, Differential Geometry, 35J, 32V,58C

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http://salesiana.dossiersoluciones.com/handle/123456789/127766

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0704.2833
 http://arxiv.org/abs/0704.2833

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arXiv