The Lin-Ni's problem for mean convex domains

Details The Lin-Ni's problem for mean convex domains The Lin-Ni's problem for mean convex domains

2011-03-19

arxiv.org/abs/1103.3811v1

Mathematics

Analysis of PDEs

To appear in "Memoirs of the AMS"

Scientific paper

We prove some refined asymptotic estimates for postive blowing 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 $\rn$, $n\geq 3$. In particular, we show that concentration can occur only on boundary points with nonpositive mean curvature when $n=3$ or $n\geq 7$. As a direct consequence, we 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.

Affiliated with

Also associated with

No associations

Rating

The Lin-Ni's problem for mean convex domains does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Lin-Ni's problem for mean convex domains, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Lin-Ni's problem for mean convex domains will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-695114