Existence results for the Yamabe problem on manifolds with boundary

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Conformal deformations to scalar-flat metrics with constant mean curvature on the boundary (2007, unknown): “The present author studied a higher dimensional case in [19], where the Weyl tensor on the boundary plays a natural role.”
An existence theorem of conformal scalar-flat metrics on manifolds with boundary (2009, background): “This concept, introduced in [Marques 2005], plays the same role that conformal normal coordinates (see [Lee and Parker 1987]) did in the case of manifolds without boundary.”