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Abstract

On a Class of Weighted Isoperimetric Inequalities †

Dipartimento di Matematica e Applicazioni R. Caccioppoli, Università di of Napoli Federico II, Via Cintia, Complesso Montesantangelo, 80126 Napoli NA, Italy
Presented at Symmetry 2017—The First International Conference on Symmetry, Barcelona, Spain, 16–18 October 2017.
Proceedings 2018, 2(1), 81; https://doi.org/10.3390/proceedings2010081
Published: 4 January 2018
(This article belongs to the Proceedings of The First International Conference on Symmetry)

Abstract

:
We study a class of isoperimetric problems on RN with respect to weights that are powers of the distance to the origin. We consider different weights in the volume and in the perimeter. We investigate cases in which, among all smooth sets Ω in RN with fixed weighted measure, the ball centered at the origin has minimum weighted perimeter. The results also imply a weighted Pólya-Szegö principle. In turn, we establish radiality of optimizers in some Caffarelli-Kohn-Nirenberg inequalities, and we obtain sharp bounds for eigenvalues of some nonlinear problems.

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MDPI and ACS Style

Posteraro, M.R. On a Class of Weighted Isoperimetric Inequalities. Proceedings 2018, 2, 81. https://doi.org/10.3390/proceedings2010081

AMA Style

Posteraro MR. On a Class of Weighted Isoperimetric Inequalities. Proceedings. 2018; 2(1):81. https://doi.org/10.3390/proceedings2010081

Chicago/Turabian Style

Posteraro, Maria Rosaria. 2018. "On a Class of Weighted Isoperimetric Inequalities" Proceedings 2, no. 1: 81. https://doi.org/10.3390/proceedings2010081

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