Nonlocal Isoperimetric Inequality

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


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.


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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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