In this paper we construct upper bounds for families of functionals of the form
Mots clés : gamma-convergence, micromagnetics, non-local energy
@article{COCV_2010__16_4_856_0, author = {Poliakovsky, Arkady}, title = {Upper bounds for a class of energies containing a non-local term}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {856--886}, publisher = {EDP-Sciences}, volume = {16}, number = {4}, year = {2010}, doi = {10.1051/cocv/2009022}, mrnumber = {2744154}, language = {en}, url = {http://www.numdam.org/articles/10.1051/cocv/2009022/} }
TY - JOUR AU - Poliakovsky, Arkady TI - Upper bounds for a class of energies containing a non-local term JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2010 SP - 856 EP - 886 VL - 16 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2009022/ DO - 10.1051/cocv/2009022 LA - en ID - COCV_2010__16_4_856_0 ER -
%0 Journal Article %A Poliakovsky, Arkady %T Upper bounds for a class of energies containing a non-local term %J ESAIM: Control, Optimisation and Calculus of Variations %D 2010 %P 856-886 %V 16 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2009022/ %R 10.1051/cocv/2009022 %G en %F COCV_2010__16_4_856_0
Poliakovsky, Arkady. Upper bounds for a class of energies containing a non-local term. ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 4, pp. 856-886. doi : 10.1051/cocv/2009022. http://www.numdam.org/articles/10.1051/cocv/2009022/
[1] Néel and cross-tie wall energies for planar micromagnetic configurations. ESAIM: COCV 8 (2002) 31-68. | Numdam | Zbl
, and ,[2] Functions of Bounded Variation and Free Discontinuity Problems, Oxford Mathematical Monographs. Oxford University Press, New York (2000). | Zbl
, and ,[3] Recent analytical developments in micromagnetics, in The Science of Hysteresis 2, G. Bertotti and I. Mayergoyz Eds., Elsevier Academic Press (2005) 269-381. | Zbl
, , and ,[4] Magnetic domains. Springer (1998).
and ,[5] Singular perturbation and the energy of folds. J. Nonlinear Sci. 10 (2000) 355-390. | Zbl
and ,[6] Upper bounds for singular perturbation problems involving gradient fields. J. Eur. Math. Soc. 9 (2007) 1-43.
,[7] Sharp upper bounds for a singular perturbation problem related to micromagnetics. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 6 (2007) 673-701. | Numdam | Zbl
,[8] A general technique to prove upper bounds for singular perturbation problems. J. Anal. Math. 104 (2008) 247-290. | Zbl
,[9] On a variational approach to the Method of Vanishing Viscosity for Conservation Laws. Adv. Math. Sci. Appl. 18 (2008) 429-451. | Zbl
,[10] Limiting domain wall energy for a problem related to micromagnetics. Comm. Pure Appl. Math. 54 (2001) 294-338. | Zbl
and ,[11] Compactness, kinetic formulation and entropies for a problem related to mocromagnetics. Comm. Partial Differential Equations 28 (2003) 249-269. | Zbl
and ,Cité par Sources :