Fundamental Solutions and Local Solvability for Nonsmooth Hormander's Operators Paperback / softback
by Marco Bramanti, Luca Brandolini, Maria Manfredini, Marco Pedroni
Part of the Memoirs of the American Mathematical Society series
Paperback / softback
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.
Information
-
Out of Stock - We are unable to provide an estimated availability date for this product
- Format:Paperback / softback
- Pages:79 pages
- Publisher:American Mathematical Society
- Publication Date:30/10/2017
- Category:
- ISBN:9781470425593
Information
-
Out of Stock - We are unable to provide an estimated availability date for this product
- Format:Paperback / softback
- Pages:79 pages
- Publisher:American Mathematical Society
- Publication Date:30/10/2017
- Category:
- ISBN:9781470425593
