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

Algebra

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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
ASIN: 1470425599
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Algebra
Domain: Amazon UK
Release Date: 30 October 2017
Listed Since: 28 June 2017

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

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