Advanced search

Browse by subject

Browse by provider

Browse by language

Content Details
Normal View
CIP View

The asymptotics of the curvature of the ...

Andersson, John...

Free

Share this content

The asymptotics of the curvature of the free discontinuity set near the cracktip for the minimizers of the Mumford-Shah functional in the plain by Andersson, John ( Author )

Content Provider	Lemonjar Open Access
Publisher	Australian National University
Publication Date	11-08-2023
Summary	We consider in 2D the following special case of the Mumford-Shah functional $$ J(u, \Gamma)=\int_{B_1\backslash\Gamma} \|\nabla u\|^2 dx + \lambda^2 \frac{\pi}{2} \mathcal{H}^1(\Gamma). $$ It is known that if the minimizer has a crack-tip 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.
ISBN	-
Item Type	Article
File Type	pdf
File Size	30.00 KB
Language	English
Subjects	-
Unlimited	MYR 0.01
Total read	-
URL	http://arxiv.org/abs/1204.5328

Citation

Review the full bibliography data and make any necessary corrections before using. Always consult your library resources for the exact formatting and punctuation guidelines.

AMA 11th EditionReferences

Andersson, John. The asymptotics of the curvature of the free discontinuity set near the cracktip for the minimizers of the Mumford-Shah functional in the plain. Australian National University. August 11, 2023. Accessed October 02, 2025. https://online.provdatabase.com/cite/15880

APA 7th EditionReferences

Andersson, John. (2023). The asymptotics of the curvature of the free discontinuity set near the cracktip for the minimizers of the Mumford-Shah functional in the plain. Australian National University. https://online.provdatabase.com/cite/15880

Chicago 17th EditionReferences

HarvardReferences

Andersson, John. (2023). The asymptotics of the curvature of the free discontinuity set near the cracktip for the minimizers of the Mumford-Shah functional in the plain. [Online]. Australian National University. Available from: https://online.provdatabase.com/cite/15880. (Accessed 02 October 2025).

Harvard AustraliaReferences

Andersson, John, 2023, The asymptotics of the curvature of the free discontinuity set near the cracktip for the minimizers of the Mumford-Shah functional in the plain, Australian National University, viewed 02 October 2025, <https://online.provdatabase.com/cite/15880>

MLA 9th EditionWorks Cited

Andersson, John. The asymptotics of the curvature of the free discontinuity set near the cracktip for the minimizers of the Mumford-Shah functional in the plain. Australian National University, 2023. PROV Database, https://online.provdatabase.com/cite/15880.

Share this eBook