Remote Access Transactions of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 35A07, 35H05

Retrieve articles in all journals with MSC: 35A07, 35H05

Additional Information

Article copyright: © Copyright 1981 American Mathematical Society

American Mathematical Society