|
Entire solutions of first-order nonlinear partial differential equations
Author(s):
Jill
E.
Hemmati
Journal:
Proc. Amer. Math. Soc.
125
(1997),
1483-1485.
MSC (1991):
Primary 35F20
MathSciNet review:
1396979
Retrieve article in:
PDF
This article is available free of charge
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:
- 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
 , 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:
10.1090/S0002-9939-97-03881-1
PII:
S 0002-9939(97)03881-1
Received by editor(s):
November 28, 1995
Communicated by:
Jeffrey B. Rauch
Copyright of article:
Copyright
1997,
American Mathematical Society
|
