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Limiting case of an isoperimetric inequality with radial density and applications

Abstract : We prove a sharp isoperimetric inequality with radial density whose functional counterpart corresponds to a limiting case for the exponents of the Il'in (or Caffarelli-Kohn-Nirenberg) inequality in L 1. We show how the latter applies to obtain an optimal critical Sobolev weighted norm improvement to one of the L 1 weighted Hardy inequalities of [25]. Further applications include an L p version with the best constant of the functional analogue of this isoperimetric inequality and also a weighted Pólya-Szegö inequality.
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https://hal.archives-ouvertes.fr/hal-02159701
Contributor : Georgios Psaradakis <>
Submitted on : Friday, December 27, 2019 - 10:39:06 PM
Last modification on : Monday, January 13, 2020 - 1:12:31 AM

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  • HAL Id : hal-02159701, version 2

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Georgios Psaradakis. Limiting case of an isoperimetric inequality with radial density and applications. 2019. ⟨hal-02159701v2⟩

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