Density estimates for a variational model driven by the Gagliardo norm

Details Density estimates for a variational model driven by the Gagliardo norm Density estimates for a variational model driven by the Gagliardo norm

2010-07-13

arxiv.org/abs/1007.2114v3

Mathematics

Analysis of PDEs

Scientific paper

We prove density estimates for level sets of minimizers of the energy $$\eps^{2s}\|u\|_{H^s(\Omega)}^2+\int_\Omega W(u)\,dx,$$ with $s \in (0,1)$, 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. As a consequence we obtain, as $\eps \to 0$, the uniform convergence of the level sets of $u$ to either a $H^s$-nonlocal minimal surface if $s\in(0,\frac 1 2)$, or to a classical minimal surface if $s \in[\frac 1 2,1)$.

Affiliated with

Also associated with

No associations

Rating

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

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-350912