Levi type extremal operators
Received: 9 September 1999
Mathematics Subject Classification (2000): 32F25
Supported by the Project M.U.R.S.T. "Geometric Properties of Real and Complex Manifolds" and by G.N.S.G.A. of C.N.R.
Abstract We introduce maximal and minimal operators L1, L2 (in the sense of Pucci) for the family FW of the "Levi type operators" L a, b on a domain W of C´R. We state some simple property for (weak, viscosity) solutions of L1, L2. In particular we prove a special form of the maximum principle. As a consequence we obtain that solutions of L1, L2 satisfy a "weak Hartogs property". We are also dealing with the Dirichlet problem for L1, L2. After shown that solutions of that provide barriers for the Levi operator we prove that this problem translates into a Dirichlet problem for a Bellman equation.