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Rearrangements of functions, maximization of convex functionals, and vortex rings

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References

  1. Adams, R.A.: Sobolev spaces. New York, San Francisco, London: AcademicPress 1975

    Google Scholar 

  2. Agmon, S.: TheL p approach to the Dirichlet problem. Ann. Sc. Norm. Super. Pisa (3)13, 405–448 (1959)

    Google Scholar 

  3. Amick, C.J., Fraenkel, L.E.: The uniqueness of Hill's spherical vortex. Arch. Ration. Mech. Anal.92, 91–119 (1986)

    Google Scholar 

  4. Bandle, C.: Isoperimetric inequalities and applications. Boston, London, Melbourne: Pitman 1980

    Google Scholar 

  5. Benjamin, T.B.: The alliance of practical and analytical insights into the nonlinear problems of fluid mechanics. Applications of methods of functional analysis to problems in mechanics 8–29. Lect. Notes Math. 503. Berlin, Heidelberg, New York: Springer 1976

    Google Scholar 

  6. Dunford, N., Schwartz, J.T.: Linear operators, Part I. New York, London: Interscience 1958

    Google Scholar 

  7. Ekeland, I., Temam, R.: Convex analysis and variational problems. Amsterdam, Oxford: North-Holland, New York: American Elsevier 1976

    Google Scholar 

  8. Fraenkel, L.E., Berger, M.S.: A global theory of steady vortex rings in an ideal fluid. Acta Math.132, 14–51 (1974)

    Google Scholar 

  9. Gilbarg, D., Trudinger, N.S.: Elliptic partial differential equations of second order. Berlin, Heidelberg, New York: Springer 1977

    Google Scholar 

  10. Halmos, P.R.: Measure theory. Princeton, New York, Toronto, London: Van Nostrand 1950

    Google Scholar 

  11. Hardy, G.H., Littlewood, J.E., Pólya, G.: Inequalities. Cambridge: Cambridge University Press 1934

    Google Scholar 

  12. Mossino, J.: Inégalités isopérimétriques et applications en physique. Paris: Hermann 1984

    Google Scholar 

  13. Mossino, J., Temam, R.: Directional derivative of the increasing rearrangement mapping and application to a queer differential equation in plasma physics. Duke Math. J.48, 475–495 (1981)

    Google Scholar 

  14. Toland, J.F.: A duality principle for non-convex optimisation and the calculus of variations. Arch. Ration. Mech. Anal.71, 41–61 (1979)

    Google Scholar 

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  1. Department of Mathematics, University College, Gower Street, WC1E 6BT, London, UK

    G. R. Burton

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  1. G. R. Burton
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Burton, G.R. Rearrangements of functions, maximization of convex functionals, and vortex rings. Math. Ann. 276, 225–253 (1987). https://doi.org/10.1007/BF01450739

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