\overline{∂}-NEUMANN PROBLEM IN THE SOBOLEV TOPOLOGY

LUIGI FONTANA STEVEN G. KRANTZ MARCO M. PELOSO

Abstract. We study the \overline{∂}-Neumann problem using the Sobolev space inner product. We show that the problem can be solved on any smoothly bounded, pseudoconvex domain. We further formulate estimates and the basic results of a Sobolev Hodge theory.