# Flat solutions and singular solutions of linear partial differential equations with analytic coefficients

Séminaire Équations aux dérivées partielles (Polytechnique) (1978-1979)

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topZachmanoglou, E. C.. "Flat solutions and singular solutions of linear partial differential equations with analytic coefficients." Séminaire Équations aux dérivées partielles (Polytechnique) (1978-1979): 1-11. <http://eudml.org/doc/111726>.

@article{Zachmanoglou1978-1979,

author = {Zachmanoglou, E. C.},

journal = {Séminaire Équations aux dérivées partielles (Polytechnique)},

keywords = {flat solutions; singular solutions; analytic coefficients; differential operator; principal symbol, characteristic surface},

language = {eng},

pages = {1-11},

publisher = {Ecole Polytechnique, Centre de Mathématiques},

title = {Flat solutions and singular solutions of linear partial differential equations with analytic coefficients},

url = {http://eudml.org/doc/111726},

year = {1978-1979},

}

TY - JOUR

AU - Zachmanoglou, E. C.

TI - Flat solutions and singular solutions of linear partial differential equations with analytic coefficients

JO - Séminaire Équations aux dérivées partielles (Polytechnique)

PY - 1978-1979

PB - Ecole Polytechnique, Centre de Mathématiques

SP - 1

EP - 11

LA - eng

KW - flat solutions; singular solutions; analytic coefficients; differential operator; principal symbol, characteristic surface

UR - http://eudml.org/doc/111726

ER -

## References

top- [1] M.S. Baouendi, F. Treves et E.C. Zachmanoglou: Flat solutions and singular solutions of homogeneous linear partial differential equations with analytic coefficients, to appear in the Duke Math. Journal. Zbl0418.35003MR534059
- [2] M S.Baouendi and E.C. Zachmanoglou: Unique continuation of solutions of partial differential equations and inequalities from manifolds of any dimension, Duke Math. Journal, 45 (1978), 1-13. Zbl0373.35001MR486484
- [3] L. Hörmander: Linear partial differential operators, Springer-Verlag, 1963. Zbl0108.09301MR404822
- [4] L. Hörmander: On the existence and the regularity of solutions of linear pseudo-differential equations. Ens. Math.17 (1971), 99-163. Zbl0224.35084MR331124
- [5] L. Hörmander: Subelliptic operators (to appear). Zbl0446.35086MR547019
- [6] L. Hörmander: Propagation of singularities and semi-global existence theorems for (pseudo-)differential operators of principal type. Annals of Math.108 (1978), 569-609. Zbl0396.35087MR512434
- [7] H. Komatsu: Irregularity of characteristic elements and construction of null solutions, Journ. Fac. Sci. Univ. Tokyo,Sec 1A, Math. 23 (1976), 298-342. Zbl0443.35009MR417546
- [8] S. Mizohata: Solutions nulles et solutions non analytiques, J. Math. Kyoto Univ.1-2 (1962), 271-302. Zbl0106.29601MR142873
- [9] T. Nagano: Linear differential systems with singularities and an application to transitive Lie algebras. J. Math. Soc. Japan18 (1966) 398-404. Zbl0147.23502MR199865
- [10] L. Nirenberg and F. Treves: On local solvability of linear PDE's Part I: Necessary conditions. Comm. Pure Appl. Math.23 (1970) 1-38. Zbl0191.39103MR264470
- [11] F. Treves: Analytic hypoelliptic P. D. E.'s of principal type, Comm. Pure Appl. Math.24 (1971), 537-570. Zbl0222.35014MR296509
- [12] E.C. Zachmanoglou: Solutions which are flat or singular on totally characteristic manifolds of first order partial differential equations. To appear in the Bulletin of the Greek Math. Soc. Zbl0459.35016MR642438
- [13] E.C. Zachmanoglou: Propagation of zeroes and uniqueness in the Cauchy problem for first order partial differential equations, Arch. Rat. Mech. Anal.38 (1970), 178-188. Zbl0199.15903MR261150

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