Why a $C^2$ domain satisfies the interior ball condition? I accept a reference too. Thank you.
2026-04-24 09:07:48.1777021668
Interior ball condition in $C^2$ domains
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Take the function $\psi$ from your previous question, A question about $C^2$ domain., and use its Taylor expansion of second order to obtain an upper bound $\psi(x)\le C|x|^2$ for small $x$. This will ensure that for small $r$, the sphere of radius $r$ centered at $re_n$, stays above the graph of this function.