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  "body": "\n## Summary\n\nA fully nonlinear PDE is a [[partial differential equation|GC5BDZ6QBC]] that depends nonlinearly on the highest-order derivatives of the unknown.\nExamples are the [[Monge–Ampère equation|14AKAC0S0T]], the [[eikonal equation|HGMX1QGTAZ]] and the [[Hamilton–Jacobi equation|5TRXQKP7DY]].\nSuch equations often lack classical solutions, and notions such as [[viscosity solutions|H1ERJ3T75T]] were developed for them.\nSee the [[definition|MTQ3SGX56W]].\n\n## Explanations\n\n### L1 human\n\nIn a fully nonlinear equation the highest derivatives are squared, multiplied together or put inside other nonlinear functions.\nFor instance, $\\abs{\\nabla u} = 1$ asks for a function whose gradient always has length $1$.\nThe distance to a closed set has this property wherever it is differentiable away from the set, but it can have corners.\nFor example, the distance to the two points $\\pm 1$ on the real line has a corner at $0$.\nSo even simple fully nonlinear equations force one to accept nonsmooth solutions.\n",
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