Anti-self-dual lagrangians : variational resolutions of non-self-adjoint equations and dissipative evolutions

Nassif Ghoussoub

Annales de l'I.H.P. Analyse non linéaire (2007)

  • Volume: 24, Issue: 2, page 171-205
  • ISSN: 0294-1449

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Ghoussoub, Nassif. "Anti-self-dual lagrangians : variational resolutions of non-self-adjoint equations and dissipative evolutions." Annales de l'I.H.P. Analyse non linéaire 24.2 (2007): 171-205. <http://eudml.org/doc/78731>.

@article{Ghoussoub2007,
author = {Ghoussoub, Nassif},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {variational formulations; non-potential boundary value problems; variational principles; variational inequalities},
language = {eng},
number = {2},
pages = {171-205},
publisher = {Elsevier},
title = {Anti-self-dual lagrangians : variational resolutions of non-self-adjoint equations and dissipative evolutions},
url = {http://eudml.org/doc/78731},
volume = {24},
year = {2007},
}

TY - JOUR
AU - Ghoussoub, Nassif
TI - Anti-self-dual lagrangians : variational resolutions of non-self-adjoint equations and dissipative evolutions
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2007
PB - Elsevier
VL - 24
IS - 2
SP - 171
EP - 205
LA - eng
KW - variational formulations; non-potential boundary value problems; variational principles; variational inequalities
UR - http://eudml.org/doc/78731
ER -

References

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  4. [4] Bardos C., Problèmes aux limites pour les equations aux dérivées partielles du premier ordre a coefficients réels ; Théorèmes d'approximation ; Application à l'équation de transport, Ann. Sci. École Norm. Sup. (4)3 (1970) 185-233. Zbl0202.36903MR274925
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  7. [7] Brezis H., Ekeland I., Un principe variationnel associé à certaines equations paraboliques. Le cas independant du temps, C. R. Acad. Sci. Paris Sér. A282 (1976) 971-974. Zbl0332.49032MR637214
  8. [8] Brezis H., Ekeland I., Un principe variationnel associé à certaines equations paraboliques. Le cas dependant du temps, C. R. Acad. Sci. Paris Sér. A282 (1976) 1197-1198. Zbl0334.35040MR637215
  9. [9] Ghoussoub N., A variational principle for non-linear transport equations, Comm. Pure Appl. Anal.4 (4) (2005) 735-742. Zbl1089.35014MR2172718
  10. [10] N. Ghoussoub, Anti-selfdual Hamiltonians: Variational resolution for Navier–Stokes equations and other nonlinear evolutions, Comm. Pure Applied Math. (2005) 25 pp., in press. 
  11. [11] N. Ghoussoub, A class of selfdual partial differential equations and its variational principles (2005), in preparation. 
  12. [12] Ghoussoub N., McCann R., A least action principle for steepest descent in a non-convex landscape, Contemp. Math.362 (2004) 177-187. Zbl1084.37060MR2091498
  13. [13] N. Ghoussoub, A. Moameni, On the existence of Hamiltonian paths connecting Lagrangian submanifolds (2005), submitted for publication. Zbl1192.37089
  14. [14] N. Ghoussoub, A. Moameni, Selfdual variational principles for periodic solutions of Hamiltonian and other dynamical systems, Comm. Partial Differential Equations (2006), in press. Zbl1130.35008MR2334832
  15. [15] N. Ghoussoub, A. Moameni, Selfduality and periodic solutions of certain Schrödinger equations and infinite dimensional Hamiltonian systems (2006), in preparation. 
  16. [16] Ghoussoub N., Tzou L., A variational principle for gradient flows, Math. Ann.30 (3) (2004) 519-549. Zbl1062.35008MR2099192
  17. [17] Ghoussoub N., Tzou L., Anti-selfdual Lagrangians II: Unbounded non self-adjoint operators and evolution equations, Ann. Mat. Pura Appl. (2005) 30, pp. Zbl1223.35023
  18. [18] N. Ghoussoub, L. Tzou, Iterations of anti-selfdual Lagrangians and applications to Hamiltonian systems and multiparameter gradient flows, Calc. Var. Partial Differential Equations (2006) 28 pp., in press. Zbl1134.49029MR2235885
  19. [19] Jost J., Riemannian Geometry and Geometric Analysis, Springer University Text, 2002. Zbl1034.53001MR1871261

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