Geodesic
Structure of entropy solutions to the eikonal equation
Journal of the European Mathematical Society, Tome 5 (2003) no. 2, pp. 107-145.

Voir la notice de l'article provenant de la source EMS Press

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.
DOI : 10.1007/s10097-002-0048-7
Classification : 49-XX, 35-XX, 00-XX
Keywords: entropy solutions, partial regularity, singular perturbation, conservation laws, rectifiability 
@article{JEMS_2003_5_2_a1,
     author = {Camillo De Lellis and Felix Otto},
     title = {Structure of entropy solutions to the eikonal equation},
     journal = {Journal of the European Mathematical Society},
     pages = {107--145},
     publisher = {mathdoc},
     volume = {5},
     number = {2},
     year = {2003},
     doi = {10.1007/s10097-002-0048-7},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10097-002-0048-7/}
}
TY  - JOUR
AU  - Camillo De Lellis
AU  - Felix Otto
TI  - Structure of entropy solutions to the eikonal equation
JO  - Journal of the European Mathematical Society
PY  - 2003
SP  - 107
EP  - 145
VL  - 5
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10097-002-0048-7/
DO  - 10.1007/s10097-002-0048-7
ID  - JEMS_2003_5_2_a1
ER  - 
%0 Journal Article
%A Camillo De Lellis
%A Felix Otto
%T Structure of entropy solutions to the eikonal equation
%J Journal of the European Mathematical Society
%D 2003
%P 107-145
%V 5
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1007/s10097-002-0048-7/
%R 10.1007/s10097-002-0048-7
%F JEMS_2003_5_2_a1
Camillo De Lellis; Felix Otto. Structure of entropy solutions to the eikonal equation. Journal of the European Mathematical Society, Tome 5 (2003) no. 2, pp. 107-145. doi : 10.1007/s10097-002-0048-7. http://geodesic.mathdoc.fr/articles/10.1007/s10097-002-0048-7/

Cité par Sources :