Bubbling on Boundary Submanifolds for the Lin-Ni-Takagi Problem at Higher Critical Exponents

Details Bubbling on Boundary Submanifolds for the Lin-Ni-Takagi Problem at Higher Critical Exponents Bubbling on Boundary Submanifolds for the Lin-Ni-Takagi Problem at Higher Critical Exponents

2011-07-27

arxiv.org/abs/1107.5566v2

Mathematics

Analysis of PDEs

57 pages

Scientific paper

We consider the equation $d^2\Delta u - u+ u^{\frac{n-k+2}{n-k-2}} =0\,\hbox{in}\Omega $, under zero Neumann boundary conditions, where $\Omega$ is open, smooth and bounded and $d$ is a small positive parameter. We assume that there is a $k$-dimensional closed, embedded minimal submanifold $K$ of $\partial\Omega$, which is non-degenerate, and certain weighted average of sectional curvatures of $\partial\Omega$ is positive along $K$. Then we prove the existence of a sequence $d=d_j\to 0$ and a positive solution $u_d$ such that $$ d^2 |\nabla u_{d} |^2 \rightharpoonup S, \delta_K \ass d \to 0 $$ in the sense of measures, where $\delta_K$ stands for the Dirac measure supported on $K$ and $S$ is a positive constant.

Affiliated with

Also associated with

No associations

Rating

Bubbling on Boundary Submanifolds for the Lin-Ni-Takagi Problem at Higher Critical Exponents 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 Bubbling on Boundary Submanifolds for the Lin-Ni-Takagi Problem at Higher Critical Exponents, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bubbling on Boundary Submanifolds for the Lin-Ni-Takagi Problem at Higher Critical Exponents will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-114015