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  "body": "\n## Summary\n\nA Lipschitz domain is an open set whose boundary is locally the graph of a [[Lipschitz|0AW1E6YTJY]] function.\nNear each boundary point the set lies on one side of the graph.\nSuch boundaries may have corners and edges, but no cusps or slits.\nLipschitz domains are the standard setting for boundary value problems with rough boundaries.\nThe divergence theorem, Sobolev traces and the theory of harmonic measure all work there.\n\n## Explanations\n\n### L1 human\n\nZoom in on any boundary point of the domain and turn your head suitably.\nYou see the domain lying above a graph whose slope is bounded.\nA square is a Lipschitz domain: at a corner the boundary looks like the graph of $\\abs{x}$ after a rotation.\nA disc with a slit is not, because near the slit the domain lies on both sides of it.\n",
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