The L2--problem on manifolds with piecewise strictly pseudoconvex boundaries

Abstract

Ever since the solution of the -Neumann problem by Kohn [4], refinements, extensions and estimates of the solution have been made by a lot of people up to the present day. Kohn discovered that, where the -Neumann problem was solvable, the space of harmonic forms is finite dimensional and it followed from Hörmander's solution [3] that on bounded pseudoconvex domains in ℂn the appropriate spaces of harmonic forms are zero dimensional.