L_2-estimates and Existence Theorems for the Exterior Differential Operators

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In this article, we obtain the notion of real-pseudoconvex domains in R^n, and we prove L_2-estimates and existence theorems for the exterior differential operators. For a real-pseudoconvex domain Ω, we have the vanishing of the de Rham cohomology H^p (Ω, R)=0, p>0. Thereby we can prove the global solvability of exterior differential equations in several spaces of functions and generalized functions in a realpseudoconvex domain in R^n. These are analogs of Poincare's Lemma in several categories.

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