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Real analytic parameter dependence of solutions of differential equations

2010
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Revista matemática iberoamericana
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We consider the problem of real analytic parameter dependence of solutions of the linear partial differential equation P (D)u = f , i.e., the question if for every family (f λ ) ⊆ D (Ω) of distributions depending in a real analytic way on λ ∈ U , U a real analytic manifold, there is a family of solutions (u λ ) ⊆ D (Ω) also depending analytically on λ such that where Ω ⊆ R d an open set. For general surjective variable coefficients operators or operators acting on currents over a smooth

doi:10.4171/rmi/599
fatcat:7xbynaicpzbszaovhzvcwfbciq