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arXiv · 2205.06588

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

Sergio Almaraz·Shaodong Wang
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Abstract

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

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Sergio Almaraz, Shaodong Wang. 2022-05-13. Energy bounds of sign-changing solutions to Yamabe equations on manifolds with boundary. https://arxiv.org/abs/2205.06588

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