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Nov 4, 2021 at 10:52 comment added Zac there are some typos in the text unfortunately, I meant $\mathbf 1_{\Omega^c}$ and $v=u-\mathbf{1}_{\Omega^c}$ above
Nov 4, 2021 at 10:51 comment added Zac Thank you so much! This was very helpful. I still have some follow-up questions, which I've included in the text of the bounty opened above
Nov 4, 2021 at 10:26 history answered Mateusz Kwaśnicki CC BY-SA 4.0