ENGLISH

The Lin-Ni's problem for mean convex domains

By Olivier Druet , Frederic Robert , Juncheng Wei

Book information

Publisher
Amer Mathematical Society
Year
2012
ISBN
0821869094, 978-0-8218-6909-3
Language
english
Format
PDF
Filesize
863 kB (883616 bytes)
Series
Memoirs of the American Mathematical Society 1027
Pages
118\118
Library
kolxoz
Time added
2015-12-12 14:00:00

Description

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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