Ukrainian Mathematical Bulletin

Volume 4, Issue 2, 2007 pp. 161-171.

Upper Bounds on Second Order Operators Acting on Metric Function

Authors: Alexander Val. Antoniouk
Author institution: Department of Nonlinear Analysis, Institute of Mathematics NAS Ukraine, Tereschenkivska 3, 01601 MSP Kiev-4, Ukraine antoniouk@imath.kiev.ua

Summary: We prove upper bounds on the general second order operator acting on metric function. The suggested approach does not use traditional formulas for deviations of geodesics and Jacobi fields construction and leads to the manifolds generalization of the classical coercitivity and dissipativity conditions for diffusion equations.

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