The Lin-Ni's Problem for Mean Convex Domains PDF
by Olivier Druet
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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.
Information
-
Download - Immediately Available
- Format:PDF
- Pages:105 pages
- Publisher:American Mathematical Society
- Publication Date:06/05/2012
- Category:
- ISBN:9780821890165
Other Formats
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Information
-
Download - Immediately Available
- Format:PDF
- Pages:105 pages
- Publisher:American Mathematical Society
- Publication Date:06/05/2012
- Category:
- ISBN:9780821890165
