Asymptotic behavior of positive solutions of some nonlinear elliptic equations on cylinders

Abstract

We establish quantitative asymptotic behavior of positive solutions of a family of nonlinear elliptic equations on the half cylinder near the end. This unifies the study of isolated singularities of some semilinear elliptic equations, such as the Yamabe equation, Hardy-Hénon equation etc.

arXiv comment29 pages, 2 figures

References in corpus (4)

• Rigidity versus symmetry breaking via nonlinear flows on cylinders and Euclidean spaces
• Asymptotic behavior of solutions to the ${\sigma }_k$-Yamabe equation near isolated singularities
• Symmetry and Asymmetry: The Method of Moving Spheres
• Isolated singularities of solutions to the Yamabe equation in dimension $6$

Cited by in corpus (1)

• Asymptotic expansion at infinity of solutions of special Lagrangian equations