Quantitative Sobolev and Hardy Inequalities, and Related Symmetrization Principles

  • Andrea Cianchi
Part of the International Mathematical Series book series (IMAT, volume 8)

This survey paper deals with strengthened forms of classical Sobolev inequalities, involving remainder terms depending on the distance from the family of extremals, and with analogues for Hardy inequalities, where extremals do not exist, but can be replaced by “virtual” extremals. An account of the stability of isoperimetric and symmetrization inequalities, on which these Sobolev and Hardy inequalities rely, is provided as well.


Sobolev Inequality Orlicz Space Isoperimetric Inequality Remainder Term Lorentz Space 
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Authors and Affiliations

  • Andrea Cianchi
    • 1
  1. 1.Università di FirenzeFirenzeItaly

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