Fundamental Solutions and Local Solvability for Nonsmooth Hormander's Operators
Sep 2017 · American Mathematical Soc.
Ebook
79
Pages
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About this ebook
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.
About the author
Marco Bramanti: Politecnico di Milano, Milano, Italy,
Luca Brandolini: Università di Bergamo, Dalmine, Italy,
Maria Manfredini: Università di Bologna, Bologna, Italy,
Marco Pedroni: Università di Bergamo, Dalmine, Italy
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