Fundamental Solutions and Local Solvability for Nonsmooth Hormander's Operators PDF Download

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Fundamental Solutions and Local Solvability for Nonsmooth Hormander's Operators

Fundamental Solutions and Local Solvability for Nonsmooth Hormander's Operators PDF Author: Marco Bramanti
Publisher: American Mathematical Soc.
ISBN: 1470425599
Category : Mathematics
Languages : en
Pages : 92

Book Description
The authors consider operators of the form in a bounded domain of where are nonsmooth Hörmander's vector fields of step such that the highest order commutators are only Hölder continuous. Applying Levi's parametrix method the authors construct a local fundamental solution for and provide growth estimates for and its first derivatives with respect to the vector fields. Requiring the existence of one more derivative of the coefficients the authors prove that also possesses second derivatives, and they deduce the local solvability of , constructing, by means of , a solution to with Hölder continuous . The authors also prove estimates on this solution.
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