Variational problems on classes of rearrangements and multiple configurations for steady vortices
Annales de l'I.H.P. Analyse non linéaire, Tome 6 (1989) no. 4, pp. 295-319.
@article{AIHPC_1989__6_4_295_0,
     author = {Burton, G. R.},
     title = {Variational problems on classes of rearrangements and multiple configurations for steady vortices},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {295--319},
     publisher = {Gauthier-Villars},
     volume = {6},
     number = {4},
     year = {1989},
     mrnumber = {998605},
     zbl = {0677.49005},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPC_1989__6_4_295_0/}
}
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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, Tome 6 (1989) no. 4, pp. 295-319. http://archive.numdam.org/item/AIHPC_1989__6_4_295_0/

[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. | MR | Zbl

[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. | Numdam | MR | Zbl

[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. | MR | Zbl

[4] J.R. Brown, Approximation Theorems for Markov Operators, Pacific J. Math., Vol. 16, 1966, pp. 13-23. | MR | Zbl

[5] G.R. Burton, Rearrangements of Functions, Maximization of Convex Functionals, and Vortex Rings, Math. Annalen, Vol. 276, 1987, pp. 225-253. | MR | Zbl

[6] J.A. Crowe, J.A. Zweibel and P.C. Rosenbloom, Rearrangements of Functions, J. Functional Analysis, Vol. 66, 1986, pp. 432-438. | MR | Zbl

[7] D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, 1977. | MR | Zbl

[8] G.H. Hardy, J.E. Littlewood and G. Pólya, Inequalities, Cambridge University Press, 1952. | MR | Zbl

[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. | MR

[10] J.B. Mcleod, Rearrangements, preprint.

[11] H.L. Royden, Real Analysis, Macmillan, 1963. | MR | Zbl

[12] J.V. Ryff, Orbits of L1-Functions under Doubly Stochastic Transformations, Trans. Amer. Math. Soc., Vol. 117, 1965, pp. 92-100. | MR | Zbl

[13] J.V. Ryff, Extreme Points of Some Convex Subsets of L1 (0, 1), Proc. Amer. Math. Soc., Vol. 18, 1967, pp. 1026-1034. | MR | Zbl

[14] J.V. Ryff, Majorized Functions and Measures, Indag. Math., Vol. 30, 1968, pp. 431-437. | MR | Zbl

[15] D.G. Schaeffer, Non-uniqueness in the Equilibrium Shape of a Confined Plasma, Comm. Partial Differential Equations, VoL 2, 1977, pp. 587-600. | MR | Zbl