Operators with Partially Analytic Coefficients

  • Nicolas LernerEmail author
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 353)


We give in this chapter an account of various results somehow interpolating between Holmgren’s theorem and Hörmander’s pseudo-convexity results. The former result uses analyticity assumptions for the whole operator, whereas the latter holds true for principally normal operators with \(C^{2}\) coefficients in the principal part, and \(L^{{\infty }}_{\text {loc}}\) for lower order terms. We shall consider operators enjoying some analytic regularity with respect to some of the variables and we shall prove a unique continuation result. We follow the papers of D. Tataru ([152, 154]), L. Hörmander ([57]), and L. Robbiano & C. Zuily ([123]).

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institut de Mathématiques de JussieuSorbonne UniversitéParisFrance

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