## Duke Mathematical Journal

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

Marek Kossowski

#### Article information

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

Dates
First available in Project Euclid: 20 February 2004

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

#### 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.