The Art of Rearranging

Abstract

Equimeasurable rearrangements of real-valued functions of one or more real variables are surveyed. We outline the development of a relevant theory over the years and some applications to mathematical analysis, calculus of variations and partial differential equations.

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1. Istituto Lombardo, Accademia di Scienze e Lettere, Milano, Italy

   Giorgio Talenti

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1. Giorgio Talenti
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Correspondence to Giorgio Talenti.

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Talenti, G. The Art of Rearranging. Milan J. Math. 84, 105–157 (2016). https://doi.org/10.1007/s00032-016-0253-6

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• Received: 16 November 2015

• Accepted: 21 January 2016

• Published: 17 March 2016

• Issue Date: June 2016

• DOI: https://doi.org/10.1007/s00032-016-0253-6

Mathematics Subject Classification

• 35A23
• 35B45
• 35J25
• 46E30
• 46E35
• 49J40

Keywords

• Super-level set
• distribution function
• rearrangements
• isoperimetric inequality
• functional inequalities
• rearrangement invariant function spaces
• variational methods
• boundary value problems for second order partial differential equations of elliptic type