Variational problems on classes of rearrangements and multiple configurations for steady vortices

G. R. Burton

Annales de l'I.H.P. Analyse non linéaire (1989)

  • Volume: 6, Issue: 4, page 295-319
  • ISSN: 0294-1449

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Burton, G. R.. "Variational problems on classes of rearrangements and multiple configurations for steady vortices." Annales de l'I.H.P. Analyse non linéaire 6.4 (1989): 295-319. <http://eudml.org/doc/78180>.

@article{Burton1989,
author = {Burton, G. R.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Mountain Pass Lemma; rearrangements; steady configurations; ideal fluid},
language = {eng},
number = {4},
pages = {295-319},
publisher = {Gauthier-Villars},
title = {Variational problems on classes of rearrangements and multiple configurations for steady vortices},
url = {http://eudml.org/doc/78180},
volume = {6},
year = {1989},
}

TY - JOUR
AU - Burton, G. R.
TI - Variational problems on classes of rearrangements and multiple configurations for steady vortices
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1989
PB - Gauthier-Villars
VL - 6
IS - 4
SP - 295
EP - 319
LA - eng
KW - Mountain Pass Lemma; rearrangements; steady configurations; ideal fluid
UR - http://eudml.org/doc/78180
ER -

References

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  1. [1] A. Ambrosetti and P.H. Rabinowitz, Dual Variational Methods in Critical Point Theory and Applications, J. Functional Analysis, Vol. 14, 1973, pp. 349-381. Zbl0273.49063MR370183
  2. [2] V.I. Arnol'd, Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l'hydrodynamique des fluides parfaits, Ann. Inst. Fourier, Grenoble, Vol. 16, 1966, pp. 319-361. Zbl0148.45301MR202082
  3. [3] T.B. Benjamin, The Alliance of Practical and Analytic Insights into the Nonlinear Problems of Fluid Mechanics. Applications of Methods of Functional Analysis to Problems in Mechanics, Lecture Notes in Math., No. 503, Springer, 1976, pp. 8-29. Zbl0369.76048MR671099
  4. [4] J.R. Brown, Approximation Theorems for Markov Operators, Pacific J. Math., Vol. 16, 1966, pp. 13-23. Zbl0139.34702MR192552
  5. [5] G.R. Burton, Rearrangements of Functions, Maximization of Convex Functionals, and Vortex Rings, Math. Annalen, Vol. 276, 1987, pp. 225-253. Zbl0592.35049MR870963
  6. [6] J.A. Crowe, J.A. Zweibel and P.C. Rosenbloom, Rearrangements of Functions, J. Functional Analysis, Vol. 66, 1986, pp. 432-438. Zbl0612.46027MR839110
  7. [7] D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, 1977. Zbl0361.35003MR473443
  8. [8] G.H. Hardy, J.E. Littlewood and G. Pólya, Inequalities, Cambridge University Press, 1952. Zbl0047.05302MR46395
  9. [9] Sir William Thomson (Lord KELVIN), Maximum and Minimum Energy in Vortex Motion, Mathematical and Physical Papers, Cambridge University Press, Vol. 4, 1910, pp. 172-183. MR1254662
  10. [10] J.B. Mcleod, Rearrangements, preprint. 
  11. [11] H.L. Royden, Real Analysis, Macmillan, 1963. Zbl0121.05501MR151555
  12. [12] J.V. Ryff, Orbits of L1-Functions under Doubly Stochastic Transformations, Trans. Amer. Math. Soc., Vol. 117, 1965, pp. 92-100. Zbl0135.18804MR209866
  13. [13] J.V. Ryff, Extreme Points of Some Convex Subsets of L1 (0, 1), Proc. Amer. Math. Soc., Vol. 18, 1967, pp. 1026-1034. Zbl0184.34503MR217586
  14. [14] J.V. Ryff, Majorized Functions and Measures, Indag. Math., Vol. 30, 1968, pp. 431-437. Zbl0164.15903MR234263
  15. [15] D.G. Schaeffer, Non-uniqueness in the Equilibrium Shape of a Confined Plasma, Comm. Partial Differential Equations, VoL 2, 1977, pp. 587-600. Zbl0371.35017MR602535

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