Limiting case of an isoperimetric inequality with radial density and applications

Georgios Psaradakis (1)

1 Universität Mannheim

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.

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]; Analyse fonctionnelle [math.FA]

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