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We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
47/2002

Structure of entropy solutions: applications to variational problems

Camillo De Lellis and Felix Otto

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.

Contact the author per mail Download full preprint 401 KB
Received:
17.06.02
Published:
17.06.02
MSC Codes:
49N60, 35D10, 35L65, 35L67
Keywords:
entropy solutions, partial regularity, singular perturbation, rectifiability, conservation laws

Related publications

inJournal
2003 Repository Open Access
Camillo De Lellis and Felix Otto

Structure of entropy solutions to the eikonal equation

In: Journal of the European Mathematical Society, 5 (2003) 2, pp. 107-145
BibTex DOI: 10.1007/s10097-002-0048-7