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Oct 26, 2021 at 12:04 vote accept MathqA
Oct 14, 2021 at 11:42 comment added Romain Gicquaud Oups, those papers prove the existence for the Dirichlet problem $u \equiv 0$ near infinity. The general case can be obtained by plugging in an approximate solution with the right boundary condition. This is how John Lee constructs his Einstein metrics. For simpler constructions, you can consult arxiv.org/abs/1109.5096 Section 4.
Oct 14, 2021 at 11:31 history answered Romain Gicquaud CC BY-SA 4.0