The asymptotics of the curvature of the free discontinuity set near the cracktip for the minimizers of the Mumford-Shah functional in the plain

Details The asymptotics of the curvature of the free discontinuity set near the cracktip for the minimizers of the Mumford-Shah functional in the plain The asymptotics of the curvature of the free discontinuity set near the cracktip for the minimizers of the Mumford-Shah functional in the plain

2012-04-24

arxiv.org/abs/1204.5328v1

Mathematics

Analysis of PDEs

"under construction", 12 pages, 3 figures

Scientific paper

We consider in 2D the following special case of the Mumford-Shah functional {equation*} J(u, \Gamma)=\int_{B_1\backslash\Gamma} |\nabla u|^2 dx + \lambda^2 \sqrt{\frac{\pi}{2}} H^1(\Gamma). {equation*} It is known that if the minimizer has a cracktip in the ball $B_1$ (assume at the origin), then $u\approx \lambda \Im \sqrt{z}$ at this point. We calculate higher order terms in the asymptotic expansion, where the homogeneity orders of those terms appear to be solutions to a certain trigonometric relation.

Affiliated with

Also associated with

No associations

Rating

The asymptotics of the curvature of the free discontinuity set near the cracktip for the minimizers of the Mumford-Shah functional in the plain 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 asymptotics of the curvature of the free discontinuity set near the cracktip for the minimizers of the Mumford-Shah functional in the plain, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The asymptotics of the curvature of the free discontinuity set near the cracktip for the minimizers of the Mumford-Shah functional in the plain will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-519648