Monge-Ampère Differential Equation
المؤلف:
Caffarelli, L. A. and Milman, M
المصدر:
Monge Ampère Equation: Applications to Geometry and Optimization.. Providence, RI: Amer. Math. Soc., 1999.
الجزء والصفحة:
...
21-7-2018
2432
Monge-Ampère Differential Equation
A second-order partial differential equation of the form
 |
(1)
|
where 
, 
, 
, 
, and 
are functions of 
, 
, 
, 
, and 
, and 
, 
, 
, 
, and 
are defined by
The solutions are given by a system of differential equations given by Iyanaga and Kawada (1980).
Other equations called the Monge-Ampère equation are
 |
(7)
|
(Moon and Spencer 1969, p. 171; Zwillinger 1997, p. 134) and
 |
(8)
|
(Gilberg and Trudinger 1983, p. 441; Zwillinger 1997, p. 134).
REFERENCES:
Caffarelli, L. A. and Milman, M. Monge Ampère Equation: Applications to Geometry and Optimization.. Providence, RI: Amer. Math. Soc., 1999.
Fairlie, D. B. and Leznov, A. N. "The General Solution of the Complex Monge-Ampère Equation in a Space of Arbitrary Dimension." 16 Sep 1999. http://arxiv.org/abs/solv-int/9909014.
Gilbarg, D. and Trudinger, N. S. Elliptic Partial Differential Equations of Second Order. Berlin: Springer-Verlag, p. 441, 1983.
Iyanaga, S. and Kawada, Y. (Eds.). "Monge-Ampère Equations." §276 in Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, pp. 879-880, 1980.
Moon, P. and Spencer, D. E. Partial Differential Equations. Lexington, MA: Heath, p. 171, 1969.
Zwillinger, D. Handbook of Differential Equations, 3rd ed. Boston, MA: Academic Press, 1997.
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