Weighted Sobolev spaces of radially symmetric functions
type: Item
instance of: scholarly article
title: Weighted Sobolev spaces of radially symmetric functions
zbMATH Open document ID: 1307.26023
author: Roberta Musina
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 2014-12-03T00:00:00Z
full work available at URL: https://arxiv.org/abs/1206.6957
review text: The paper under review is devoted to the investigation of the following inequalities \[ \int\limits_{{\mathbb R}^n} |x|^{\alpha}|\nabla^ku|^p~\!dx\geq c\int\limits_{{\mathbb R}^n} |x|^{\alpha-kp}|u|^p~\!dx, \] \[ \int_{{\mathbb R}^n} |x|^{\alpha}|\Delta^m u|^p dx\geq c \int_{{\mathbb R}^n} |x|^{\alpha-p}|\nabla(\Delta^{m-1}u)|^{p }dx \] on the spaces of radially symmetric functions. The author discusses the existence of extremals and in some cases computes the best constants.
reviewed by: Michael Perelmuter
Mathematics Subject Classification ID: 26D10
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 47F05
Mathematics Subject Classification ID: 35J30
zbMATH DE Number: 6376695
zbMATH Keywords: Rellich inequality
zbMATH Keywords: Sobolev inequality
zbMATH Keywords: Caffarelli-Kohn-Nirenberg inequality
zbMATH Keywords: weighted biharmonic operator
zbMATH Keywords: dilation invariance
MaRDI profile type: Publication
OpenAlex ID: W3099502893
arXiv ID: 1206.6957
cites work: Optimal Hardy--Rellich inequalities, maximum principle and related eigenvalue problem
cites work: GENERALIZED HARDY–RELLICH INEQUALITIES IN CRITICAL DIMENSION AND ITS APPLICATIONS
cites work: Problèmes isoperimetriques et espaces de Sobolev
cites work: SYMMETRY BREAKING OF EXTREMAL FUNCTIONS FOR THE CAFFARELLI– KOHN–NIRENBERG INEQUALITIES
cites work: Q3676658
cites work: Radial and non radial solutions for Hardy-Hénon type elliptic systems
cites work: On Caffarelli-Kohn-Nirenberg-type inequalities for the weighted biharmonic operator in cones
cites work: Rellich inequalities with weights
cites work: A Class of Second-order Dilation Invariant Inequalities
cites work: On the Caffarelli-Kohn-Nirenberg inequalities: sharp constants, existence (and nonexistence), and symmetry of extremal functions.
cites work: Sobolev spaces of symmetric functions and applications
cites work: Hardy inequalities with optimal constants and remainder terms
cites work: Polyharmonic boundary value problems. Positivity preserving and nonlinear higher order elliptic equations in bounded domains
cites work: Bessel pairs and optimal Hardy and Hardy-Rellich inequalities
cites work: Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities
cites work: Symétrie et compacité dans les espaces de Sobolev
cites work: A simple approach to Hardy inequalities
cites work: Optimal weighted Hardy-Rellich inequalities on H 2 ∩ H 0 1
cites work: Ground state solutions of a critical problem involving cylindrical weights
cites work: Radially symmetric solutions to the Hénon–Lane–Emden system on the critical hyperbola
cites work: Q3661978
cites work: Q3238502
cites work: Q5571936
cites work: The existence of minimal immersions of 2-spheres
cites work: Q3251547
cites work: Best constant in Sobolev inequality
cites work: Sharp constant in a Sobolev inequality
DOI: 10.1007/S10231-013-0348-4
description: scientific article