PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1999 | 50 | 1 | 179-194
Tytuł artykułu

Classification of Monge-Ampère equations with two variables

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper deals with the classification of hyperbolic Monge-Ampère equations on a two-dimensional manifold. We solve the local equivalence problem with respect to the contact transformation group assuming that the equation is of general position nondegenerate type. As an application we formulate a new method of finding symmetries. This together with previous author's results allows to state the solution of the classical S. Lie equivalence problem for the Monge-Ampère equations.
Słowa kluczowe
Rocznik
Tom
50
Numer
1
Strony
179-194
Opis fizyczny
Daty
wydano
1999
Twórcy
  • Chair of Mathematical Modeling, Baumann Moscow State Technological University, P.O.Box 546, 119618, Moscow, Russia
Bibliografia
  • [AG] V. I. Arnol'd, A. B. Givental', Symplectic geometry, in: Dynamical Systems IV, Encyclopaedia Math. Sci. 4, Springer, Berlin, 1990, 1-136.
  • [Au] T. Aubin, Nonlinear Analysis on Manifolds. Monge-Ampère Equations, Grundlehren Math. Wiss. 252, Springer, New York, 1982.
  • [FN] A. Frölicher, A. Nijenhuis, Theory of vector-valued differential forms I, Nederl. Akad. Wetensch. Proc. Ser. A 59 = Indag. Math. 18 (1956), 338-359.
  • [G] E. Goursat, Leçons sur l'intégration des équations aux dérivées partielles du second ordre à deux variables independantes, tome I, Hermann, Paris, 1896.
  • [Ha] J. Haantjes, On $X_m$-forming sets of eigenvectors, Nederl. Akad. Wetensch. Proc. Ser. A 58 = Indag. Math. 17 (1955), 158-162.
  • [KLV] I. Krasil'shchik, V. Lychagin, A. Vinogradov, Geometry of jet spaces and nonlinear partial differential equations, Adv. Stud. Contemp. Math. 1, Gordon and Breach, New York, 1986.
  • [Kr1] B. S. Kruglikov, Some classificational problems in four dimensional geometry: distributions, almost complex structures and Monge-Ampère equations (in Russian), Mat. Sb. 189 no. 11 (1998), 61-74; e-print: http:/xxx.lanl.gov/abs/dg-ga/9611005.
  • [Kr2] B. S. Kruglikov, Symplectic and contact Lie algebras with an application to Monge-Ampère equations (in Russian), Trudy Mat. Inst. Steklov 221 (1998), 232-246; e-print: http:/xxx.lanl.gov/abs/dg-ga/9709004.
  • [Ku] A. Kushner, Symplectic geometry of mixed type equations, in: The Interplay between Differential Geometry and Differential Equations, V. V. Lychagin (ed.), Amer. Math. Soc. Transl. ser. 2, 167, Amer. Math. Soc., Providence, 1995, 131-142.
  • [Lie] S. Lie, Gesammelte Abhandlungen, Band VI, Aschehoug, Oslo, and Teubner, Leipzig, 1922.
  • [Ly1] V. V. Lychagin, Contact geometry and nonlinear second order differential equations, Uspekhi Mat. Nauk 34 no. 1 (1979), 137-165 (in Russian); English transl.: Russian Math. Surveys 34 (1979), 149-180.
  • [Ly2] V. Lychagin, Lectures on Geometry of Differential Equations, Ciclo di conferenze tenute presso il Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate Università 'La Sapienza', Roma, 1992.
  • [LRC] V. V. Lychagin, V. N. Rubtsov, I. V. Chekalov, A classification of Monge-Ampère equations, Ann. Sci. École Norm. Sup. (4) 26 (1993), 281-308.
  • [M] T. Morimoto, Le problème d'équivalence des équations de Monge-Ampère, C. R. Acad. Sci. Paris Sér. A-B 289 (1979), A25-A28.
  • [NN] A. Newlander, L. Nirenberg, Complex analytic coordinates in almost-complex manifolds, Ann. Math. (2) 65 (1957), 391-404.
  • [R] A. Rakhimov, Singularities of Riemann invariants, Funktsional. Anal. i Prilozhen. 27 no. 1 (1993), 46-59 (in Russian); English transl.: Funct. Anal. Appl. 27 (1993), 39-50.
  • [S] S. Sternberg, Lectures on Differential Geometry, Prentice-Hall, Englewood Cliffs, 1964.
  • [T] N. Tanaka, On differential systems, graded Lie algebras and pseudogroups, J. Math. Kyoto Univ. 10 (1970), 1-82.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv50z1p179bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.