Minimax Theory and its Applications 07 (2022), No. 2, 173--184
Copyright Heldermann Verlag 2022
An Upper Bound for the Least Energy of a Nodal Solution to the Yamabe Equation on the Sphere
Mónica Clapp
Instituto de Matemáticas, Universidad Nacional Autónoma de México, Ciudad de México
monica.clapp@im.unam.mx
Angela Pistoia
Dipartimento SBAI, La Sapienza Università di Roma, Italy
angela.pistoia@uniroma1.it
Tobias Weth
Institut für Mathematik, Goethe-Universität, Fankfurt am Main, Germany
weth@math.uni-frankfurt.de
[Abstract-pdf]
For each $n\geq 3$ we establish the existence of a nodal solution $u$ to the Yamabe problem on the round sphere $(\mathbb{S}^n,g)$ which satisfies $$\int_{\mathbb{S}^n}|u|^{2^*}dV_g < 2m_n\mathrm{vol}(\mathbb{S}^n),$$ where $m_3=9$, $m_4= 7$, $m_5=m_6=6$, and $m_n= 5$ if $n\geq 7$.
Keywords: Yamabe equation, nodal solutions, energy bounds.
MSC: 58J05, 35B06, 35B33.
[ Fulltext-pdf (201 KB)] for subscribers only.