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We study the Yamabe equation in the Euclidean half-space. We prove that anysign-changing solution has at least twice the energy of a standard bubble.Moreover, a sharper energy lower bound of the sign-changing solution set isalso established via the method of moving planes. This bound increases theenergy range for which Palais-Smale sequences of related variational problemhas a non-trivial weak limit.

Energy bounds of sign-changing solutions to Yamabe equations on manifolds with boundary