structural:summarization
Functions of several variables

For example, if φ (x, y) {\displaystyle \varphi (x,y)} denotes the displacement of a membrane above the domain D {\displaystyle D} in the x, y {\displaystyle x,y} plane, then its potential energy is proportional to its surface area:

Plateau's problem consists of finding a function that minimizes the surface area while assuming prescribed values on the boundary of D {\displaystyle D}; the solutions are called minimal surfaces. The Euler–Lagrange equation for this problem is nonlinear:

See Courant (1950) for details.