Fundamental Solutions and Local Solvability for Nonsmooth Hormander's Operators
Seiten
2017
American Mathematical Society (Verlag)
978-1-4704-2559-3 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-2559-3 (ISBN)
- Titel z.Zt. nicht lieferbar
- Versandkostenfrei innerhalb Deutschlands
- Auch auf Rechnung
- Verfügbarkeit in der Filiale vor Ort prüfen
- Artikel merken
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 |
Haben Sie eine Frage zum Produkt? |
Mehr entdecken
aus dem Bereich
aus dem Bereich