Eikonal Blog

2010.08.12

Uses of Eikonal approximation

Filed under: eikonal approximation, mathematics, physics — Tags: — sandokan65 @ 14:41
  • “Rytov/Eikonal Approximation of Wavepaths” by William S. Harlan (1998.04) – http://billharlan.com/pub/papers/rytov/rytov.html
  • “Structure of entropy solutions to the eikonal equation” by Camillo De Lellis and Felix Otto (Journal: J. Eur. Math. Soc.; Volume: 5; Number: 2; Pages: 107-145; 2003) – http://cvgmt.sns.it/papers/delott02/
      Abstract: In this paper, we establish rectifiability of the jump set of an S1-valued conservation law in two space-dimensions. This conservation law is a reformulation of the eikonal equation and is motivated by the singular limit of a class of variational problems. The only assumption on the weak solutions is that the entropy productions are (signed) Radon measures, an assumption which is justified by the variational origin. The methods are a combination of Geometric Measure Theory and elementary geometric arguments used to classify blow-ups.
      The merit of our approach is that we obtain the structure as if the solutions were in BV, without using the BV-control, which is not available in these variationally motivated problems.
Advertisements

Leave a Comment »

No comments yet.

RSS feed for comments on this post. TrackBack URI

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

Create a free website or blog at WordPress.com.

%d bloggers like this: