Existence and Approximation of Solutions to a Linear Partial Differential Equation

Abstract

In this section, we denote by Ω an open subset of the Euclidean space Rⁿ and by P, a differential operator (i.e., a linear partial differential operator with C^∞ coefficients) in Ω. However, all the statements and results extend, with appropriate but obvious adaptations (in particular, concerning duality), to the case where Ω is a C^∞ manifold, countable at infinity, and P a V-W-differential operator in Ω, V, W denoting two finite dimensional complex vector bundles over Ω.