TY  - BOOK
AU  - Bramanti,Marco
AU  - Brandolini,Luca
AU  - Manfredini,Maria
AU  - Pedroni,Marco
TI  - Fundamental solutions and local solvability for nonsmooth Hormander's operators
T2  - Memoirs of the American Mathematical Society
SN  - 9781470425593 (alk. paper)
U1  - 510 23
PY  - 2017///
CY  - Providence : 
PB  - American Mathematical Society, 
KW  - Differential operators
KW  - Nonsmooth optimization
KW  - Vector fields
N1  - Includes bibliographical references; 1. Introduction --
2. Some known results about nonsmooth Hörmander's vector fields --
3. Geometric estimates --
4. The parametrix method --
5. Further regularity of the fundamental solution and local solvability of L --
6. Appendix: Examples of nonsmooth Hörmander's operators satisfying assumptions A or B --
Bibliography
N2  - 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 Hörmander's vector fields of step r such that the highest order commutators are only Hölder 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
ER  -