Assembling a rearrangement

descriptionPublicationkeyboard_double_arrow_right Article , Part of book or chapter of book 01 Jan 1987 English Publisher:Springer Science and Business Media LLCJournal:Archive for Rational Mechanics and Analysis, volume 98, pages 285-293 (issn: 0003-9527, eissn: 1432-0673,

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Authors: Talenti, Giorgio;

doi: 10.1007/bf00276910 , 10.1007/978-3-642-83743-2_28

Assembling a rearrangement

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Abstract

The author presents an algorithm which transforms a function u: [0,\(\ell]\to {\mathbb{R}}\) into its monotone decreasing rearrangement \(u^*\). His construction is motivated by a nice heuristical argument from the buoyant convection of a liquid with variable density. Mathematically this leads to a free boundary problem for a first order quasilinear equation.

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University of Florence
Italy

Keywords

first order quasilinear equation, PDEs with low regular coefficients and/or low regular data, algorithm, rearrangement, buoyant convection of a liquid, Free boundary problems for PDEs, General first-order partial differential equations and systems of first-order partial differential equations, free boundary problem

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