GIUSEPPE TOMASSINI

Levi type extremal operators

Pages 101-116
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 F_W 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.