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Fundamental Solutions and Local Solvability for Nonsmooth Hormander's Operators (Memoirs of the American Mathematical Society)

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Description

About the Author Marco Bramanti, Politecnico di Milano, Italy.Luca Brandolini, Universita di Bergamo, Dalmine, Italy.Maria Manfredini, Universita di Bologna, Italy.Marco Pedroni, Universita di Bergamo, Dalmine, Italy. Product Description The authors consider operators of the form $L=\sum_{i=1}^{n}X_{i}^{2}+X_{0}$ in a bounded domain of $\mathbb{R}^{p}$ where $X_{0},X_{1},\ldots,X_{n}$ are nonsmooth Hormander's vector fields of step $r$ such that the highest order commutators are only Holder continuous. Applying Levi's parametrix method the authors construct a local fundamental solution $\gamma$ for $L$ and provide growth estimates for $\gamma$ and its first derivatives with respect to the vector fields. Requiring the existence of one more derivative of the coefficients the authors prove that $\gamma$ also possesses second derivatives, and they deduce the local solvability of $L$, constructing, by means of $\gamma$, a solution to $Lu=f$ with Holder continuous $f$. The authors also prove $C_{X,loc}^{2,\alpha}$ estimates on this solution.

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Format
paperback
Domain
Amazon UK
Release Date
30 October 2017
Listed Since
28 June 2017

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