Fundamental Solutions and Local Solvability for Nonsmooth Hormander's Operators

Marco Bramanti, Luca Brandolini, Maria Manfredini, Marco Pedroni (Autoren)

Buch | Softcover

79 Seiten

2017
American Mathematical Society (Verlag)
978-1-4704-2559-3 (ISBN)

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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.

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.

Introduction
Some known results about nonsmooth Hormander's vector fields
Geometric estimates
The parametrix method
Further regularity of the fundamental solution and local solvability of $L$
Appendix. Examples of nonsmooth Hormander's operators satisfying assumptions A or B
Bibliography.

Erscheinungsdatum	12.10.2017
Reihe/Serie	Memoirs of the American Mathematical Society
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Gewicht	160 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
ISBN-10	1-4704-2559-9 / 1470425599
ISBN-13	978-1-4704-2559-3 / 9781470425593
Zustand	Neuware