I am reading a paper where they assume the boundary of a domain is "Analytic". They never define it. Is this a standard definition, and, if so, what is it?
2026-05-05 07:49:14.1777967354
What does it mean for a boundary to be analytic in the context of a PDE?
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Yes, it is a standard definition. It means that locally you can find coordinates for which the boundary looks like the graph of an analytic function. In other words, given $x \in \partial \Omega$, there is a radius $r$ and an analytic function $f$ such that, up to a rotation, $$\partial \Omega \cap B(x,r) = \{y \in B(x,r) : y_n = f(y_1,\dots,y_{n-1})\}.$$