Sharp Global Bounds for the Hessian on Pseudo-Hermitian Manifolds

Details Sharp Global Bounds for the Hessian on Pseudo-Hermitian Manifolds Sharp Global Bounds for the Hessian on Pseudo-Hermitian Manifolds

2007-04-21

arxiv.org/abs/0704.2833v1

Mathematics

Analysis of PDEs

13 pages

Scientific paper

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.

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