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Quantitative Sobolev and Hardy Inequalities, and Related Symmetrization Principles

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Sobolev Spaces In Mathematics I

Part of the book series: International Mathematical 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.

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Authors and Affiliations

  1. Università di Firenze, Piazza Ghiberti 27, Firenze, 50122, Italy

    Andrea Cianchi

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  1. Andrea Cianchi
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Editors and Affiliations

  1. Department of Mathematics, Ohio State University, Columbus, USA

    Vladimir Maz’ya

  2. Department of Mathematical Sciences, University of Liverpool, Liverpool, UK

    Vladimir Maz’ya

  3. Department of Mathematics, Linköping University, Linköping, Sweden

    Vladimir Maz’ya

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Cianchi, A. (2009). Quantitative Sobolev and Hardy Inequalities, and Related Symmetrization Principles. In: Maz’ya, V. (eds) Sobolev Spaces In Mathematics I. International Mathematical Series, vol 8. Springer, New York, NY. https://doi.org/10.1007/978-0-387-85648-3_4

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