论文标题
符号改变解决方案的能量界限到具有边界的歧管上的Yamabe方程
Energy bounds of sign-changing solutions to Yamabe equations on manifolds with boundary
论文作者
论文摘要
我们研究欧几里得半空间中的Yamabe方程。我们证明，任何改变标志的解决方案的能量至少是标准气泡的能量的两倍。此外，还通过移动平面的方法建立了签名解决方案集的更清晰的能量下限。这种结合增加了相关变分问题的palais-smale序列的能量范围。
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.
