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$\begingroup$ Thanks for writing up a formal argument, a pleasure to read. (Though I admit that having done only so much math, it takes effort for someone like me to understand well, but I got the key idea of the argument) $\endgroup$

biquart
– biquart

2024-10-04 15:19:05 +00:00
Commented Oct 4, 2024 at 15:19
$\begingroup$ @jmichael I have updated the answer since, notably my assumption that $\nabla g(p) = 0$ cannot occur on regions of non-zero measure was false and I have provided a counterexample. The initial counterexample was not provided by me: math.stackexchange.com/a/4980330/463794 This means that you have to make sure that your SDBF has a non-zero gradient almost everywhere on $\partial\Omega$, otherwise you can run into degenerate cases w.r.t. the normal. $\endgroup$

lightxbulb
– lightxbulb

2024-10-04 23:10:59 +00:00
Commented Oct 4, 2024 at 23:10

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