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Nonlocal Minimal Surfaces and Nonlocal Curvature

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

Abstract

Recall that if a set E has minimal local perimeter in a bounded set Ω, then it has zero mean curvature at each point of ∂E ∩ Ω (see [51]), and the equation that says that the curvature is equal to zero is the Euler–Lagrange equation associated to the minimization of the perimeter of a set.

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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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