Variational formulation of Schrödinger-Poisson systems in dimension d ≤ 3

Francis Nier

Journées équations aux dérivées partielles (1992)

  • page 1-10
  • ISSN: 0752-0360

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Nier, Francis. "Formulation variationnelle de systèmes Schrödinger-Poisson en dimension $d\le 3$." Journées équations aux dérivées partielles (1992): 1-10. <http://eudml.org/doc/93249>.

@article{Nier1992,
author = {Nier, Francis},
journal = {Journées équations aux dérivées partielles},
keywords = {nonlinear Schrödinger-Poisson systems; equilibrium of electron gas},
language = {fre},
pages = {1-10},
publisher = {Ecole polytechnique},
title = {Formulation variationnelle de systèmes Schrödinger-Poisson en dimension $d\le 3$},
url = {http://eudml.org/doc/93249},
year = {1992},
}

TY - JOUR
AU - Nier, Francis
TI - Formulation variationnelle de systèmes Schrödinger-Poisson en dimension $d\le 3$
JO - Journées équations aux dérivées partielles
PY - 1992
PB - Ecole polytechnique
SP - 1
EP - 10
LA - fre
KW - nonlinear Schrödinger-Poisson systems; equilibrium of electron gas
UR - http://eudml.org/doc/93249
ER -

References

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  1. [1] A. Adams, Sobolev Spaces, Academic Press, New-York, (1975). Zbl0314.46030
  2. [2] S. Agmon, Spectral Properties of Schrödinger Operators and Scattering Theory, Ann. Scuola Normale di Pisa 2 2 (1975), 151-218. Zbl0315.47007MR53 #1053
  3. [3] J. Chazarain, A. Piriou, Introduction à la théorie des équations aux dérivées partielles linéaires, Gauthiers-Villars, Paris (1981). Zbl0446.35001MR82i:35001
  4. [4] C. Gérard, Sharp propagation estimates for N-particles systems, Preprint-CMAT Ecole Polytechnique (1990). Zbl0760.35049
  5. [5] B. Helffer, J. Sjöstrand, Equation de Harper, Lect. Notes in Physics, Springer 345 (1989), 118-197. Zbl0699.35189
  6. [6] T. Kerkhoven, A. T. Galick, V. Ravaioli, J. H. Arends, Y. Saad, Efficient numerical simulation of electrons states in quantum wires, J. Appl. Phys. 68 (1990), 3461-3469. 
  7. [7] F. Nier, A Variational Formulation of Schrödinger-Poisson Systems in Dimension d ≤ 3, Techn. Report # 136, Purdue University, Rapport interne du CMAP N 253, Ecole Polytechnique, submitted to Commun. in PDE. Zbl0785.35086
  8. [8] F. Nier, Schrödinger-Poisson Systems in Dimension d ≤ 3 : the Whole-Space Case, manuscript. Zbl0807.35119
  9. [9] L. Nirenberg, On elliptic partial differential equations, Ann. Scuola Sup. Pisa 13 (1959), 116-162. Zbl0088.07601MR22 #823
  10. [10] M. Reed, B. Simon, Methods of Modern Mathematical Physics, Academic Press, New-York, San Francisco, Londres (1975). Zbl0308.47002
  11. [11] B. Simon, Trace Ideals and Applications, Cambridge University Press (1978). 
  12. [12] B. Vinter, Subbands and charge control in a two-dimensional electron gas field effect transistor, Appl. Phy. Let. 44 (1987), P. 307. 

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