Uniqueness in the Cauchy problem for a class of hypoelliptic ultraparabolic operators
Chiara Cinti
Università di Bologna, Italy

Abstract
We consider a class of hypoelliptic ultraparabolic operators in the form
\[ \L=\sum_{j=1}^m X_j^2+X_0-\partial_t, \]under the assumption that the vector fields and are invariant with respect to a suitable homogeneous Lie group . We show that if are two solutions of \( \L u = 0 \) on \( \RN \times ]0,T[ \) and , then each of the following conditions: can be bounded by , or both and are non negative, implies . We use a technique which relies on a pointwise estimate of the fundamental solution of \( \L \).
Cite this article
Chiara Cinti, Uniqueness in the Cauchy problem for a class of hypoelliptic ultraparabolic operators. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 20 (2009), no. 2, pp. 145–158
DOI 10.4171/RLM/538