Geometric structure of magnetic walls
Lecumberry, Myriam1
1 Université de Nantes Laboratoire de Mathématiques Jean Leray UFR Sciences et Techniques 2 rue de la Houssinière 44322 Nantes Cedex 3
Journées équations aux dérivées partielles (2005), article no. 1, 11 p.

After a short introduction on micromagnetism, we will focus on a scalar micromagnetic model. The problem, which is hyperbolic, can be viewed as a problem of Hamilton-Jacobi, and, similarly to conservation laws, it admits a kinetic formulation. We will use both points of view, together with tools from geometric measure theory, to prove the rectifiability of the singular set of micromagnetic configurations.

DOI : 10.5802/jedp.14
Lecumberry, Myriam 1

1 Université de Nantes Laboratoire de Mathématiques Jean Leray UFR Sciences et Techniques 2 rue de la Houssinière 44322 Nantes Cedex 3 
@article{JEDP_2005____A1_0,
     author = {Lecumberry, Myriam},
     title = {Geometric structure of magnetic walls},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {1},
     pages = {1--11},
     publisher = {Groupement de recherche 2434 du CNRS},
     year = {2005},
     doi = {10.5802/jedp.14},
     mrnumber = {2352770},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/jedp.14/}
}
TY  - JOUR
AU  - Lecumberry, Myriam
TI  - Geometric structure of magnetic walls
JO  - Journées équations aux dérivées partielles
PY  - 2005
SP  - 1
EP  - 11
PB  - Groupement de recherche 2434 du CNRS
UR  - http://www.numdam.org/articles/10.5802/jedp.14/
DO  - 10.5802/jedp.14
LA  - en
ID  - JEDP_2005____A1_0
ER  - 
%0 Journal Article
%A Lecumberry, Myriam
%T Geometric structure of magnetic walls
%J Journées équations aux dérivées partielles
%D 2005
%P 1-11
%I Groupement de recherche 2434 du CNRS
%U http://www.numdam.org/articles/10.5802/jedp.14/
%R 10.5802/jedp.14
%G en
%F JEDP_2005____A1_0
Lecumberry, Myriam. Geometric structure of magnetic walls. Journées équations aux dérivées partielles (2005), article  no. 1, 11 p. doi : 10.5802/jedp.14. http://www.numdam.org/articles/10.5802/jedp.14/

[ADM] L. Ambrosio, C. De Lellis and C. Mantegazza, Line energies for gradient vector fields in the plane, Calc. Var. PDE 9 (1999) 4, 327-355. | MR | Zbl

[AFP] L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems, Oxford Science Publications, (2000). | MR | Zbl

[AKLR] L. Ambrosio, B. Kirchheim, M. Lecumberry and T. Rivière, On the rectifiability of defect measures arising in micromagnetic domains, Nonlinear problems in mathematical physics and related topics, II, 29-60, Int. Math. Ser. (N.Y.), 2. KluwerPlenum, New York, (2002). | MR | Zbl

[ALR] L. Ambrosio, M. Lecumberry and T. Riviere, A viscosity property of minimizing micromagnetic configurations, Comm. Pure Appl. Math. 56 (2003), no 6, 681-688. | MR | Zbl

[DO] C. De Lellis and F. Otto, Structure of entropy solutions: applications to variational problems, to appear in J. Europ. Math. Soc..

[DOW] C. De Lellis, F. Otto and M. Westdickenberg, Structure of entropy solutions for multi-dimensional conservation laws, to appear in Arch. Ration. Mech. Anal. | Zbl

[DR] C. De Lellis and T. Rivière, Concentration estimates for entropy measures, to appear in J. Math. Pures et Appl..

[HS] A. Hubert and A. Schäfer, Magnetic domains: the analysis of magnetic microstructures, Springer, Berlin-New York, (1998).

[LR] M. Lecumberry and T. Rivière, The rectifiability of shock waves for the solutions of genuinely non-linear scalar conservation laws in 1+1 D., Preprint (2002).

[Ri] T. Rivière, Parois et vortex en micromagnétisme, Journées “Equations aux dérivées partielles” (Forges-les-Eaux, 2002), Exp. no XIV. | Numdam | MR

[RS1] T. Rivière and S. Serfaty, Limiting Domain Wall Energy for a Problem Related to Micromagnetics, Comm. Pure Appl. Math., 54, (2001), 294-338. | MR | Zbl

[RS2] T. Rivière and S. Serfaty, Compactness, kinetic formulation and entropies for a problem related to micromagnetics, Comm. Partial Differential Equations 28 (2003), no 1-2, 249-269. | MR | Zbl

[Se] D. Serre, Systèmes de lois de conservation I, Diderot, (1996). | MR | Zbl

Cité par Sources :