CodiceQDD 155
TitoloFundamental solutions and local solvability for nonsmooth Hörmander s operators
Autore/iBramanti, M.; Brandolini, L.; Manfredini, M.; Pedroni, M.
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AbstractWe consider operators of the form $L= sum_{i=1}^{n}X_{i}^{2}+X_{0}$ in a bounded domain of 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 we 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 we prove that gamma also possesses second derivatives, and we deduce the local solvability of L, constructing, by means of gamma, a solution to Lu=f with H older continuous f. We also prove $C_{X,loc}^{2, alpha}$ estimates on this solution.