The partial differential equation
(Gray 1997, p. 399), whose solutions are called minimal surfaces. This corresponds to the mean curvature equalling 0 over the surface.
d'Alembert's equation
is sometimes also known as Lagrange's equation (Zwillinger 1997, pp. 120 and 265-268).
See also
d'Alembert's Equation,
Mean Curvature,
Minimal
Surface
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References
do Carmo, M. P. "Minimal Surfaces." §3.5 in Mathematical
Models from the Collections of Universities and Museums (Ed. G. Fischer).
Braunschweig, Germany: Vieweg, pp. 41-43, 1986.Gray, A. Modern
Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca
Raton, FL: CRC Press, 1997.Zwillinger, D. "Lagrange's Equation."
§II.A.69 in Handbook
of Differential Equations, 3rd ed. Boston, MA: Academic Press, pp. 120
and 265-268, 1997.Referenced on Wolfram|Alpha
Lagrange's Equation
Cite this as:
Weisstein, Eric W. "Lagrange's Equation."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LagrangesEquation.html
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