Fundamental solutions and local solvability for nonsmooth Hormander's operators / Marco Bramanti...[et al.].

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.

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.