Manifolds of nonanalyticity of solutions of certain linear PDEs
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- by E. C. Zachmanoglou PDF
- Trans. Amer. Math. Soc. 266 (1981), 573-582 Request permission
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
- 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, DOI 10.1215/S0012-7094-79-04618-0
- Lars Hörmander (ed.), Seminar on Singularities of Solutions of Linear Partial Differential Equations, Annals of Mathematics Studies, No. 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
Additional Information
- © Copyright 1981 American Mathematical Society
- 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