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- W2110603404 abstract "where =(n+2)=(n− 2) is the critical Sobolev exponent, = n=(n− 2) is the critical Sobolev exponent on the boundary, is the unit outer normal of @ and H (x) is the mean curvature. This problem is related to the Yamabe problem on manifolds with boundary, see [7, 8]. It was proved in [7, 8] that, if either K(x)≡ 1; h(x)≡ 0; or K(x)≡ 0; h(x)≡ 1; then Eq. (1.1) has a classical solution which minimizes the Yamabe ratio. When K(x) 6≡ 0; h(x) 6≡ 0; it is natural to seek for the Nehari minimizers. This idea works when is not conformal to a ball, see [9]. However, when is a ball the situation is very di erent. In fact, for certain functions K(x) and h(x), Eq. (1.1) has no positive solution at all. Therefore, solvability conditions on K(x) and h(x) are needed. To make it more clear, we consider the Yamabe equation" @default.
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- W2110603404 modified "2023-10-04" @default.
- W2110603404 title "Yamabe equations on half-spaces" @default.
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