Estimates for the -Neumann problem and nonexistence of C2 Levi-flat hypersurfaces in

Abstract

Let Ω be a pseudoconvex domain with C2 boundary in Open image in new window , n ≥ 2. We prove that the Open image in new window -Neumann operator N exists for square-integrable forms on Ω. Furthermore, there exists a number e0>0 such that the operators Open image in new window and the Bergman projection are regular in the Sobolev space We ( Ω) for e 0 and n ≥ 2. As a consequence, we prove the nonexistence of C2 Levi-flat hypersurfaces in Open image in new window .