Fundamental solutions and local solvability for nonsmooth Hörmander's operators - Bramanti, Marco, 1963-; Brandolini, Luca, 1963-; Manfredini, Maria, 1967-; Pedroni, Marco, 1964- (Memoirs of the American Mathematical Society ;, 2017)
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}, …, 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 γ for L and provide growth estimates for γ and its first derivatives with respect to the vector fields. Requiring the existence of one more derivative of the coefficients the authors prove that γ also possesses second derivatives, and the.