arXiv Analytics

Sign in

arXiv:1901.11263 [math.AP]AbstractReferencesReviewsResources

Axially symmetric solutions of Allen-Cahn equation with finite Morse index

Changfeng Gui, Kelei Wang, Juncheng Wei

Published 2019-01-31Version 1

In this paper we study axially symmetric solutions of Allen-Cahn equation with finite Morse index. It is shown that there does not exist such a solution in dimensions between $4$ and $10$. In dimension $3$, we prove that these solutions have finitely many ends. Furthermore, the solution has exactly two ends if its Morse index equals $1$.

Comments: 19 pages; comments are welcome
Categories: math.AP
Related articles: Most relevant | Search more
arXiv:1102.4022 [math.AP] (Published 2011-02-19)
Even Symmetry of Some Entire Solutions to the Allen-Cahn Equation in Two Dimensions
arXiv:1710.00526 [math.AP] (Published 2017-10-02)
Convergence of the Allen-Cahn equation with Neumann boundary condition on non-convex domains
arXiv:1701.04119 [math.AP] (Published 2017-01-15)
Liouville-type theorems with finite Morse index for Δ_λ-Laplace operator

Links

Toolbox