Resolution of $$\partial \bar {\partial }$$ for Differential Forms with Boundary Value in the Sense of Currents Defined on a Half Space of $$\mathbb {C}^{n}$$

Abstract

AbstractWe solve the \(\partial \bar {\partial }\) for the differential forms of class C ∞ with boundary value in the sense of currents defined on an unbounded Levi-flat domain of \(\mathbb {C}^n\) whose the interior of complementary is also Levi-flat and unbounded. Example \(\Omega = \{ z= (z_1, \cdots , z_n) \in \mathbb {C}^n : Im(z_n) > 0 \}\).KeywordsThe \(\partial \bar {\partial }\) operatorThe De Rham cohomologyExtensible currentsBoundary value