Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Entire solutions of first-order
nonlinear partial differential equations


Author: Jill E. Hemmati
Journal: Proc. Amer. Math. Soc. 125 (1997), 1483-1485
MSC (1991): Primary 35F20
DOI: https://doi.org/10.1090/S0002-9939-97-03881-1
MathSciNet review: 1396979
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We show that any entire solution of an essentially nonlinear first-order partial differential equation in two variables must be linear.


References [Enhancements On Off] (What's this?)

  • 1. S. Bernstein, Über ein geometrisches Theorem und seine Anwendung auf die partiellen Differentialgleichungen vom elliptischen Typus, Math. Z. 26 (1927), 551-558.
  • 2. L. Bers, Isolated singularities of minimal surfaces, Ann. of Math. (2) 53 (1951), 364-380. MR 13:244c
  • 3. F. John, Partial Differential Equations, 4th ed., Springer-Verlag, New York, 1982. MR 80f:35001 (3rd ed.)
  • 4. K. Jörgens, Über die Lösungen der Differentialgleichung $rt-s^2=1$, Math. Ann. 127 (1954), 130-134. MR 15:961e
  • 5. D. Khavinson, A note on entire solutions of the eiconal equation, Amer. Math. Monthly 102 (1995), 159-161. MR 95j:35132
  • 6. S. G. Krantz, Function Theory of Several Complex Variables, Wiley, 1982. MR 84c:32001
  • 7. G. Letac and J. Pradines, Seules les affinités préservent les lois normales, C. R. Acad. Sci. Paris Sér. A 286 (1978), 399-402. MR 57:14100
  • 8. E. J. Mickle, A remark on a theorem of Serge Bernstein, Proc. Amer. Math. Soc. 1 (1950), 86-89. MR 12:13f
  • 9. J. C. C. Nitsche, Elementary proof of Bernstein's theorem on minimal surfaces, Ann. of Math. (2) 66 (1957), 593-594. MR 19:878f
  • 10. J. C. C. Nitsche, Lectures on Minimal Surfaces. Vol. 1, Cambridge University Press, 1989. MR 90m:49031
  • 11. T. Rado, Zu einem Satze von S.Bernstein über Minimalflächen im Gromen, Math. Z. 26 (1927), 559-565.
  • 12. O. N. Stavroudis and R. C. Fronczek, Caustic surfaces and the structure of the geometrical image, J. Opt. Soc. Amer. 66 (1976), 795-800. MR 54:11984

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 35F20

Retrieve articles in all journals with MSC (1991): 35F20


Additional Information

Jill E. Hemmati
Affiliation: Department of Mathematics, University of Arkansas, Fayetteville, Arkansas 72701

DOI: https://doi.org/10.1090/S0002-9939-97-03881-1
Received by editor(s): November 28, 1995
Communicated by: Jeffrey B. Rauch
Article copyright: © Copyright 1997 American Mathematical Society

American Mathematical Society