Hypoelliptic operators with characteristic variety of codimension two and the wave equation

R. B. Melrose

Séminaire Équations aux dérivées partielles (Polytechnique) (1979-1980)

  • page 1-12

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Melrose, R. B.. "Hypoelliptic operators with characteristic variety of codimension two and the wave equation." Séminaire Équations aux dérivées partielles (Polytechnique) (1979-1980): 1-12. <http://eudml.org/doc/111745>.

@article{Melrose1979-1980,
author = {Melrose, R. B.},
journal = {Séminaire Équations aux dérivées partielles (Polytechnique)},
keywords = {characteristic variety; propagation of singularities; hypoelliptic operator; Hermite transformation},
language = {eng},
pages = {1-12},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {Hypoelliptic operators with characteristic variety of codimension two and the wave equation},
url = {http://eudml.org/doc/111745},
year = {1979-1980},
}

TY - JOUR
AU - Melrose, R. B.
TI - Hypoelliptic operators with characteristic variety of codimension two and the wave equation
JO - Séminaire Équations aux dérivées partielles (Polytechnique)
PY - 1979-1980
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 12
LA - eng
KW - characteristic variety; propagation of singularities; hypoelliptic operator; Hermite transformation
UR - http://eudml.org/doc/111745
ER -

References

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  1. [1] L. Boutet de Monvel: Hypoelliptic operators with double characteristics and related pseudodifferential operators. Comm. Pure Appl.27 (1974), 585-639. Zbl0294.35020MR370271
  2. [2] C. Caratheodory: Variationsrechnung und partielle Differentialgleichnugen. Teubner, Berlin1935. Zbl0011.35603JFM61.0547.01
  3. [3] J. Chazarain: Formule de Poisson pour les variétés riemanniennes. Invent. Math.24 (1974), 65-82. Zbl0281.35028MR343320
  4. [4] J.J. Duistermaat and V.W. Guillemin: The spectrum of positive elliptic operators and closed bicharacteristics. Invent. Math.29 (1975), 39-79. Zbl0307.35071MR405514
  5. [6] L. Hörmander: The spectral function of an elliptic operator. Acta Math.121 (1968), 193-218. Zbl0164.13201MR609014
  6. [7] L. Hörmander: The Cauchy problem for differential equations with double characteristics. J. D'Analyse Math.32 (1977), 118-196. Zbl0367.35054MR492751
  7. [8] V. Ia Ivrii and V.M. Petkov: Necessary conditions for the correctness of the Cauchy problem for non-strictly hyperbolic equations. Uspehi Mat. Nauk.29 (1974), 3-70. Zbl0312.35049MR427843
  8. [9] P.D. Lax: Asymptotic solutions of oscillatory initial value problems. Duke Math. J.24 (1957), 627-646. Zbl0083.31801MR97628
  9. [10] A. Menikoff and J. Sjöstrand: On the eigenvalues of a class of hypoelliptic operators. Math. Ann.235 (1978), 55-85. The eigenvalues of hypoelliptic operators III - the non-semibounded case. J. d'Analyse Math.35 (1979), 123-150, Zbl0436.35065MR481627
  10. [11] R.B. Melrose: The wave equation for a hypoelliptic operator with symplectic characteristics of codimension two. In preparation. Zbl0599.35139
  11. [12] B. Lascar: Propagation des singularités pour des équations hyperboliques à caractéristique de multiplicité au plus double et singularités masloviennes. Zbl0506.35067
  12. [13] B. Helffer: Sur l'hypoellipticité des opérateurs pseudodifférentiels à caractéristiques multiples (perte de 3/2 dérivées). Math. Ann.217 (1975) 165-188. 
  13. [14] A. Grigis: Propagation des singularités pour des opérateurs pseudodifférentiels à caractéristiques doubles (to appear). Zbl0494.35088MR546643

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