Lagrange's Equation

The Partial Differential Equation

$$(1+{f_y}^2)f_{xx}+2f_xf_yf_{xy}+(1+{f_x}^2)f_{yy}=0,$$

whose solutions are called Minimal Surfaces.

See also Minimal Surface

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.