Vetenskap & teknik
Pocket
The Lin-Ni's Problem for Mean Convex Domains
Olivier Druet • Frederic Robert • Juncheng Wei
1549:-
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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.
- Format: Pocket/Paperback
- ISBN: 9780821869093
- Språk: Engelska
- Antal sidor: 105
- Utgivningsdatum: 2012-06-30
- Förlag: American Mathematical Society