Memoirs of the American Mathematical Society

2 total works

The Lin-Ni's Problem for Mean Convex Domains

by Olivier Druet, Frederic Robert, and Juncheng Wei

Published 1 July 2012

The authors prove some refined asymptotic estimates for positive blow-up solutions to $\Delta u+\epsilon u=n(n-2)u^{\frac{n+2}{n-2}}$ on $\Omega$, $\partial_\nu u=0$ on $\partial\Omega$, $\Omega$ being a smooth bounded domain of $\mathbb{R}^n$, $n\geq 3$. In particular, they show that concentration can occur only on boundary points with nonpositive mean curvature when $n=3$ or $n\geq 7$. As a direct consequence, they prove the validity of the Lin-Ni's conjecture in dimension $n=3$ and $n\geq 7$ for mean convex domains and with bounded energy. Recent examples by Wang-Wei-Yan show that the bound on the energy is a necessary condition.

On Non-Topological Solutions of the A_2 and B_2 Chern-Simons System

by Weiwei Ao, Chang-Shou Lin, and Juncheng Wei

Published 1 January 2016

Volume 239, number 1132 (fourth of 6 numbers), January 2016.