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  "body": "\n## Summary\n\nThe Calderón projector of an elliptic differential operator $P$ on a domain $\\Omega$ is a projection acting on boundary data.\nIts range is exactly the set of Cauchy data on $\\partial\\Omega$ of the solutions of $Pu = 0$ in $\\Omega$.\nIt is a matrix of [[pseudo-differential operators|FF27N0BWTP]] on the boundary.\nIt reduces boundary value problems in $\\Omega$ to equations on $\\partial\\Omega$, and it is the tool behind the general theory of [[elliptic boundary value problems|C1F7T523G0]].\n\n## Explanations\n\n### L1 human\n\nA solution of an elliptic equation inside a region leaves a trace on the boundary: its values and its normal derivatives there.\nNot every list of boundary data comes from a solution, because the interior equation imposes a hidden relation between them.\nThe Calderón projector is a projection that keeps the boundary data of solutions unchanged and sends every list of boundary data to the data of some solution.\nFor the Laplacian in the plane, the data are a pair $(f, g)$ of the boundary values and the normal derivative.\nThe projector fixes the pairs $(u|_{\\partial\\Omega}, \\partial_\\nu u|_{\\partial\\Omega})$ of [[harmonic functions|0DEB0JMN0W]] $u$ and sends every other pair to such a pair.\n",
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