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Nonlocal Isoperimetric Inequality

  • José M. Mazón
  • Julio Daniel Rossi
  • J. Julián Toledo
Chapter
Part of the Frontiers in Mathematics book series (FM)

Abstract

For the nonlocal perimeter, there is also an isoperimetric inequality, and here the main hypothesis used on J is that it is radially nonincreasing.

Its proof uses the symmetric decreasing rearrangement, which replaces a given nonnegative function f by a radial function f. Let us recall briefly the definition and some basic properties of this rearrangement.

References

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    F. Andreu, J.M. Mazón, J.D. Rossi, J. Toledo, A nonlocal p-Laplacian evolution equation with Neumann boundary conditions. J. Math. Pures Appl. 90, 201–227 (2008)MathSciNetCrossRefGoogle Scholar
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    G.H. Hardy, J.E. Littlewood, G. Polya, Inequalities (Cambridge University Press, Cambridge, 1952)zbMATHGoogle Scholar
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    E.H. Lieb, M. Loss, Analysis. AMS Graduate Studies in Mathematics, vol. 14 (American Mathematical Society, Providence, 1987)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • José M. Mazón
    • 1
  • Julio Daniel Rossi
    • 2
  • J. Julián Toledo
    • 3
  1. 1.Departamento de Análisis MatemáticoUniversitat de ValènciaValenciaSpain
  2. 2.Departamento de MatemáticasUniversidad de Buenos AiresBuenos AiresArgentina
  3. 3.Departamento de Análisis MatemáticoUniversitat de ValènciaValènciaSpain

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