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.
Myriam Lecumberry. Geometric structure of magnetic walls. Journées équations aux dérivées partielles (2005), article no. 1, 11 p.. doi: 10.5802/jedp.14
@incollection{JEDP_2005____A1_0,
author = {Myriam Lecumberry},
title = {Geometric structure of magnetic walls},
booktitle = {},
series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
eid = {1},
pages = {1--11},
year = {2005},
publisher = {Groupement de recherche 2434 du CNRS},
doi = {10.5802/jedp.14},
mrnumber = {2352770},
language = {en},
url = {https://proceedings.centre-mersenne.org/articles/10.5802/jedp.14/}
}
TY - JOUR AU - Myriam Lecumberry 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 - https://proceedings.centre-mersenne.org/articles/10.5802/jedp.14/ DO - 10.5802/jedp.14 LA - en ID - JEDP_2005____A1_0 ER -
%0 Journal Article %A Myriam Lecumberry %T Geometric structure of magnetic walls %J Journées équations aux dérivées partielles %] 1 %D 2005 %P 1-11 %I Groupement de recherche 2434 du CNRS %U https://proceedings.centre-mersenne.org/articles/10.5802/jedp.14/ %R 10.5802/jedp.14 %G en %F JEDP_2005____A1_0
[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. | Zbl | MR
[AFP] L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems, Oxford Science Publications, (2000). | Zbl | MR
[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). | Zbl | MR
[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. | Zbl | MR
[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. | MR | Numdam
[RS1] T. Rivière and S. Serfaty, Limiting Domain Wall Energy for a Problem Related to Micromagnetics, Comm. Pure Appl. Math., 54, (2001), 294-338. | Zbl | MR
[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. | Zbl | MR
[Se] D. Serre, Systèmes de lois de conservation I, Diderot, (1996). | Zbl | MR
Cité par Sources :