Extension of solutions for Monge-Ampère equations of hyperbolic type

Mikio Tsuji

Banach Center Publications (1996)

  • Volume: 33, Issue: 1, page 437-447
  • ISSN: 0137-6934

How to cite

top

Tsuji, Mikio. "Extension of solutions for Monge-Ampère equations of hyperbolic type." Banach Center Publications 33.1 (1996): 437-447. <http://eudml.org/doc/262541>.

@article{Tsuji1996,
author = {Tsuji, Mikio},
journal = {Banach Center Publications},
keywords = {Monge-Ampère equations},
language = {eng},
number = {1},
pages = {437-447},
title = {Extension of solutions for Monge-Ampère equations of hyperbolic type},
url = {http://eudml.org/doc/262541},
volume = {33},
year = {1996},
}

TY - JOUR
AU - Tsuji, Mikio
TI - Extension of solutions for Monge-Ampère equations of hyperbolic type
JO - Banach Center Publications
PY - 1996
VL - 33
IS - 1
SP - 437
EP - 447
LA - eng
KW - Monge-Ampère equations
UR - http://eudml.org/doc/262541
ER -

References

top
  1. [1] R. Courant and D. Hilbert, Methods of Mathematical Physics, Vol. 2, Interscience, New York, 1962. Zbl0099.29504
  2. [2] G. Darboux, Leçons sur la théorie générale des surfaces, tome 3, Gauthier-Villars, Paris, 1894. 
  3. [3] E. Goursat, Leçons sur l'intégration des équations aux dérivées partielles du second ordre, tome 1, Hermann, Paris, 1932. 
  4. [4] E. Goursat, Cours d'analyse mathématique, tome 3, Gauthier-Villars, Paris, 1927. Zbl53.0180.05
  5. [5] J. Hadamard, Le problème de Cauchy et les équations aux dérivées partielles linéaires hyperboliques, Hermann, Paris, 1932. Zbl58.0519.16
  6. [6] S. Izumiya, Geometric singularities for Hamilton-Jacobi equation, in: Adv. Stud. Pure Math. 22, 1993, 89-100. Zbl0837.35090
  7. [7] S. Izumiya and G. T. Kossioris, Semi-local classification of geometric singularities for Hamilton-Jacobi equations, preprint. Zbl0837.35091
  8. [8] H. Lewy, Über das Anfangswertproblem bei einer hyperbolischen nichtlinearen partiellen Differentialgleichung zweiter Ordnung mit zwei unabhängigen Veränderlichen, Math. Ann. 98 (1928), 179-191. Zbl53.0473.15
  9. [9] H. Lewy, A priori limitations for solutions of Monge-Ampère equations I, II, Trans. Amer. Math. Soc. 37 (1934), 417-434; 41 (1937), 365-374. Zbl61.0513.02
  10. [10] V. V. Lychagin, Contact geometry and non-linear second order differential equations, Russian Math. Surveys 34 (1979), 149-180. Zbl0427.58002
  11. [11] T. Morimoto, La géométrie des équations de Monge-Ampère, C. R. Acad. Sci. Paris 289 (1979), 25-28. Zbl0425.35023
  12. [12] S. Nakane, Formation of singularities for Hamilton-Jacobi equations in several space variables, J. Math. Soc. Japan 43 (1991), 89-100. Zbl0743.35043
  13. [13] S. Nakane, Formation of shocks for a single conservation law, SIAM J. Math. Anal. 19 (1988), 1391-1408. Zbl0681.35057
  14. [14] A. Pliś, Caharacteristic of nonlinear partial differential equations, Bull. Acad. Polon. Sci. Cl. III 2 (1954), 419-422. 
  15. [15] M. Tsuji, Formation of singularities for Hamilton-Jacobi equation II, J. Math. Kyoto Univ. 26 (1986), 299-308. Zbl0655.35009
  16. [16] M. Tsuji, Prolongation of classical solutions and singularities of generalized solutions, Ann. Inst. H. Poincaré Anal. Non Linéaire 7 (1990), 505-523. Zbl0722.35025
  17. [17] H. Whitney, On singularities of mappings of Euclidean spaces I, Ann. of Math. 62 (1955), 374-410. Zbl0068.37101

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.