Kristaly, A. (2020) Proceedings of the Royal Society of Edinburgh Section A - Mathematics [Matematică, Q2]

Publicat: 06 Noiembrie 2020

Kristaly, A. (2020) Nodal solutions for the fractional Yamabe problem on Heisenberg groups. Proceedings of the Royal Society of Edinburgh Section A - Mathematics, 150(2), 771-788.

DOI: https://doi.org/10.1017/prm.2018.95

✓ Publisher: Cambridge University Press
✓ Web of Science Core Collection: Science Citation Index Expanded
✓ Categories: Mathematics, Applied; Mathematics
✓ Article Influence Score (AIS): 0.975 (2020) / Q2 in all categories

Abstract: We prove that the fractional Yamabe equation ${\rm {\cal L}}_\gamma u = \vert u \vert <^>{((4\gamma )/(Q-2\gamma ))}u$ on the Heisenberg group & x210d;(n) has [n + 1/2] sequences of nodal (sign-changing) weak solutions whose elements have mutually different nodal properties, where ${\rm {\cal L}}_\gamma $ denotes the CR fractional sub-Laplacian operator on & x210d;(n), Q = 2n + 2 is the homogeneous dimension of & x210d;(n), and $\gamma \in \bigcup\nolimits_{k = 1}<^>n [k,((kQ)/Q-1)))$. Our argument is variational, based on a Ding-type conformal pulling-back transformation of the original problem into a problem on the CR sphere S2n + 1 combined with a suitable Hebey-Vaugon-type compactness result and group-theoretical constructions for special subgroups of the unitary group U(n + 1).

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