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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Manifolds of nonanalyticity of solutions of certain linear PDEs


Author: E. C. Zachmanoglou
Journal: Trans. Amer. Math. Soc. 266 (1981), 573-582
MSC: Primary 35A07; Secondary 35H05
MathSciNet review: 617552
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Abstract: It is shown that if $ P$ is a linear partial differential operator with analytic coefficients, and if $ M$ is an analytic manifold of codimension $ 3$ which is partially characteristic with respect to $ P$ and satisfies certain additional conditions, then one can find, in a neighborhood of any point of $ M$, solutions of the equation $ Pu = 0$ which are flat or singular precisely on $ M$.


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  • [1] M. S. Baouendi, F. Trevés, and E. C. Zachmanoglou, Flat solutions and singular solutions of homogeneous linear partial differential equations with analytic coefficients, Duke Math. J. 46 (1979), no. 2, 409–440. MR 534059
  • [2] Lars Hörmander (ed.), Seminar on Singularities of Solutions of Linear Partial Differential Equations, Annals of Mathematics Studies, vol. 91, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1979. Held at the Institute for Advanced Study, Princeton, N.J., 1977/78. MR 547013

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DOI: https://doi.org/10.1090/S0002-9947-1981-0617552-1
Article copyright: © Copyright 1981 American Mathematical Society