Duke Mathematical Journal

Local existence and stability of multivalued solutions to determined analytic first-order systems on the plane

Marek Kossowski

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

Source
Duke Math. J., Volume 69, Number 3 (1993), 635-661.

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1077293730

Digital Object Identifier
doi:10.1215/S0012-7094-93-06926-8

Mathematical Reviews number (MathSciNet)
MR1208814

Zentralblatt MATH identifier
0785.35019

Subjects
Primary: 35A07
Secondary: 35D05 58C27

Citation

Kossowski, Marek. Local existence and stability of multivalued solutions to determined analytic first-order systems on the plane. Duke Math. J. 69 (1993), no. 3, 635--661. doi:10.1215/S0012-7094-93-06926-8. https://projecteuclid.org/euclid.dmj/1077293730


Export citation

References

  • [B] R. L. Bryant, The geometry of $J^1(M^2,N^2)$, personal notes.
  • [C] S. S. Chern, et al., Exterior differential systems, M.S.R.I. publication, 1989.
  • [CF] R. Courant and K. O. Friedrichs, Supersonic Flow and Shock Waves, Appl. Math. Sci., vol. 21, Springer-Verlag, New York, 1985.
  • [Cr] E. Cartan, Exterior Differential Systems and their Geometric Applications, Hermann, Paris, 1971.
  • [D] L. Dresner, Similarity Solutions of Nonlinear Partial Differential Equations, Pitman Res. Notes in Math. Ser., vol. 88, Longman Sci. Tech., Harlow, 1983.
  • [EL] D. Eisenbud and H. Levine, An algebraic formula for the degree of a $C^\infty$ map germ, Ann. of Math. (2) 106 (1977), no. 1, 19–44.
  • [G] V. Guillemin, Cosmology in $(2 + 1)$-dimensions, cyclic models, and deformations of $M\sb 2,1$, Annals of Mathematics Studies, vol. 121, Princeton University Press, Princeton, NJ, 1989.
  • [GG] M. Golubitsky and V. Guillemin, Stable Mappings and their Singularities, Grad. Texts in Math., vol. 14, Springer-Verlag, New York, 1973.
  • [Gr] R. B. Gardner, A differential geometric generalization of characteristics, Comm. Pure Appl. Math. 22 (1969), 597–626.
  • [GS] V. Guillemin and S. Sternberg, Symplectic Techniques in Physics, Cambridge Univ. Press, Cambridge, 1984.
  • [H] M. Hirsch, Differential Topology, Grad. Texts in Math., vol. 33, Springer-Verlag, New York, 1990.
  • [K] M. Kossowski, Local existence of multivalued solutions to analytic symplectic Monge-Ampère equations, Indiana Univ. Math. J. 40 (1991), no. 1, 123–148.
  • [V] I. S. Krasilshchik, V. V. Lychagin, and A. M. Vinogradov, Geometry of Jet Spaces and Nonlinear Partial Differential Equations, Adv. Stud. Contemp. Math., vol. 1, Gordon & Breach, New York, 1986.
  • [YI] K. Yano and S. Ishihara, Tangent and Cotangent Bundles: Differential Geometry, Pure Appl. Math., vol. 16, Dekker, New York, 1973.