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Transactions of the American Mathematical Society

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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
DOI: https://doi.org/10.1090/S0002-9947-1981-0617552-1
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$.


References [Enhancements On Off] (What's this?)

  • [1] M. S. Baouendi, F. Treves and E. C. Zachmanoglou, Flat solutions and singular solutions of homogeneous linear partial differential equations with analytic coefficients, Duke Math. J. 46 (1979), 409-440. MR 534059 (80h:35034)
  • [2] L. Hörmander, Subelliptic operators, Seminar on Singularities of Solutions of Linear Partial Differential Equations (L. Hörmander, Ed.), Ann. of Math. Studies, no. 91, Princeton Univ. Press, Princeton, N. J., 1979. MR 547013 (80g:35003)

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

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