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  "body": "\n## Summary\n\nThe minimal surface equation for a function $u$ of $n$ variables says that its graph is a [[minimal surface|41X0YW2R9N]].\nThat is, the graph has zero mean curvature.\nIt reads $\\operatorname{div}\\big(\\nabla u / \\sqrt{1 + \\abs{\\nabla u}^2}\\big) = 0$.\nIt is the Euler–Lagrange equation of the area of the graph, $\\int \\sqrt{1 + \\abs{\\nabla u}^2} \\, dx$.\nIt is a model [[quasilinear|7X9N9H3RK6]] elliptic equation, and its study led to Bernstein's problem and to deep results on regularity.\n\n## Explanations\n\n### L1 human\n\nImagine a soap film over a wire frame, seen as the graph of a height function $u(x, y)$.\nThe film settles where its area cannot be lowered by small changes, and this condition is a differential equation for the height.\nFor gentle slopes, the equation is close to Laplace's equation $u_{xx} + u_{yy} = 0$.\nPlanes are the simplest solutions, and Scherk's surface $u(x, y) = \\log(\\cos y / \\cos x)$ is a famous curved one.\n",
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