It takes the average reader 1 hour and 47 minutes to read The Lin-Ni's Problem for Mean Convex Domains by Olivier Druet
Assuming a reading speed of 250 words per minute. Learn more
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.
The Lin-Ni's Problem for Mean Convex Domains by Olivier Druet is 105 pages long, and a total of 26,775 words.
This makes it 35% the length of the average book. It also has 33% more words than the average book.
The average oral reading speed is 183 words per minute. This means it takes 2 hours and 26 minutes to read The Lin-Ni's Problem for Mean Convex Domains aloud.
The Lin-Ni's Problem for Mean Convex Domains is suitable for students ages 10 and up.
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