Does there exist an extension operator: $\mathbb{E}: BV\left(\partial B(x_0, R); \mathbb{R}^N\right)\mapsto BV\left( B(x_0, R); \mathbb{R}^N\right)$ ?
Hopefully one of you can help! Thanks.
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$\begingroup$ would the trivial extension work $(Eu)(x_0 + v) = u(x_0 + R v/\|v\|)$ ? $\endgroup$daw– daw2025-12-03 21:20:57 +00:00Commented Dec 3 at 21:20
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$\begingroup$ Thank you. Could you explain it in more detail? $\endgroup$Rio Nguyen– Rio Nguyen2025-12-04 16:33:47 +00:00Commented Dec 4 at 16:33
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