Fundamental Solutions and Local Solvability for Nonsmooth Hoermander's Operators (eBook)

Marco Bramanti (Autor)

eBook Download: PDF

79 Seiten
American Mathematical Society (Verlag)
978-1-4704-4131-9 (ISBN)

Infos

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 Hoermander's vector fields of step $r$ such that the highest order commutators are only Hoelder 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 Hoelder continuous $f$. The authors also prove $C_{X,loc}^{2,/alpha}$ estimates on this solution.

Produkt-Details

• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• ISBN-10: 1-4704-4131-4 / 1470441314
• ISBN-13: 978-1-4704-4131-9 / 9781470441319