Density estimates for a nonlocal variational model via the Sobolev inequality

Details Density estimates for a nonlocal variational model via the Sobolev inequality Density estimates for a nonlocal variational model via the Sobolev inequality

2011-03-31

arxiv.org/abs/1103.6205v1

Mathematics

Analysis of PDEs

Scientific paper

We consider the minimizers of the energy $$ \|u\|_{H^s(\Omega)}^2+\int_\Omega W(u)\,dx,$$ with $s \in (0,1/2)$, where $\|u\|_{H^s(\Omega)}$ denotes the total contribution from $\Omega$ in the $H^s$ norm of $u$, and $W$ is a double-well potential. By using a fractional Sobolev inequality, we give a new proof of the fact that the sublevel sets of a minimizer $u$ in a large ball $B_R$ occupy a volume comparable with the volume of $B_R$.

Affiliated with

Also associated with

No associations

Rating

Density estimates for a nonlocal variational model via the Sobolev inequality 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 Density estimates for a nonlocal variational model via the Sobolev inequality, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Density estimates for a nonlocal variational model via the Sobolev inequality will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-245674