The Lin-Ni's problem for mean convex domains
著者
書誌事項
The Lin-Ni's problem for mean convex domains
（Memoirs of the American Mathematical Society, no. 1027）
American Mathematical Society, 2012, c2011
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注記
"July 2012, volume 218, number 1027 (end of volume)"--T.p
Includes bibliography (p. 103-105)
内容説明・目次
内容説明
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.
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