Access to the text (HTML) Access to the text (HTML)
PDF Access to the PDF text

Access to the full text of this article requires a subscription.
  • If you are a subscriber, please sign in 'My Account' at the top right of the screen.

  • If you want to subscribe to this journal, see our rates

  • You can purchase this item in Pay Per ViewPay per View - FAQ : 30,00 € Taxes included to order
    Pages Iconography Videos Other
    5 0 0 0

Comptes Rendus Mathématique
Volume 350, n° 9-10
pages 475-479 (mai 2012)
Doi : 10.1016/j.crma.2012.04.020
Received : 20 April 2012 ;  accepted : 27 April 2012
Optimal Hardy-type inequalities for elliptic operators
Sur des inégalités de Hardy optimales

Baptiste Devyver a , Martin Fraas b , Yehuda Pinchover a
a Department of Mathematics, Technion - Israel Institute of Technology, Haifa, 32000, Israel 
b Theoretische Physik ETH Zürich, Wolfgang-Pauli-Str. 27, 8093 Zürich, Switzerland 


For a general second order elliptic operator P in a domain Ω , we construct a Hardy weight W in the punctured domain   such that   is subcritical in   for  , null-critical in   for  , and supercritical near infinity and near 0 for  . Our method is based on the theory of positive solutions and applies to both symmetric and nonsymmetric operators. The constructed Hardy weight is given by an explicit formula involving the Green function of P and its gradient.

The full text of this article is available in PDF format.

Soit P un opérateur elliptique du second ordre sur un domaine Ω . On construit un poids W , tel que si   est un domaine épointé, alors   est sous-critique sur   pour  , nul-critique dans   pour  , et supercritique à lʼinfini et en 0 pour  . Notre approche repose sur la théorie des solutions positives dʼun opérateur elliptique du second ordre, et sʼapplique à la fois au cas symétrique et non symétrique. Le poids est de plus donné par une formule explicite faisant intervenir la fonction de Green de P et son gradient.

The full text of this article is available in PDF format.

© 2012  Published by Elsevier Masson SAS de la part de Académie des sciences.
EM-CONSULTE.COM is registrered at the CNIL, déclaration n° 1286925.
As per the Law relating to information storage and personal integrity, you have the right to oppose (art 26 of that law), access (art 34 of that law) and rectify (art 36 of that law) your personal data. You may thus request that your data, should it be inaccurate, incomplete, unclear, outdated, not be used or stored, be corrected, clarified, updated or deleted.
Personal information regarding our website's visitors, including their identity, is confidential.
The owners of this website hereby guarantee to respect the legal confidentiality conditions, applicable in France, and not to disclose this data to third parties.
Article Outline
You can move this window by clicking on the headline