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
    3 0 0 0

Comptes Rendus Mathématique
Volume 348, n° 9-10
pages 513-515 (mai 2010)
Doi : 10.1016/j.crma.2010.03.019
accepted : 23 Mars 2010
On some inequalities of Bourgain, Brezis, Maz’ya, and Shaposhnikova related to   vector fields
Sur certaines inégalités de Bourgain, Brezis, Maz’ya et Shaposhnikova concernant les champs de vecteurs dans  

Petru Mironescu
Université de Lyon, Université Lyon 1, CNRS, UMR 5208 Institut Camille-Jordan, bâtiment du Doyen Jean-Braconnier, 43, boulevard du 11 novembre 1918, 69200 Villeurbanne cedex, France 


Bourgain and Brezis established, for maps   with zero average, the existence of a solution   of (1)  . Maz’ya proved that if, in addition,  , then (1) can be solved in  . Their arguments are quite different. We present an elementary property of fundamental solutions of the biharmonic operator in two dimensions. This property unifies, in two dimensions, the two approaches, and implies another (apparently unrelated) estimate of Maz’ya and Shaposhnikova. We discuss higher dimensional analogs of the above results.

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

Bourgain and Brezis ont montré que, si   est de moyenne nulle, alors (1)   a une solution  . Maz’ya a prouvé que si, de plus, on a  , alors il existe une solution de (1) dans  . Les deux preuves sont distinctes. Dans cette note, nous présentons une propriété élémentaire des solutions fondamentales de l’opérateur biharmonique en dimension deux. Cette propriété unifie, en dimension deux, les approches de Bourgain–Brezis et Maz’ya, et implique une autre estimation de Maz’ya et Shaposhnikova (apparemment non liée aux précédentes). Nous discutons des variantes de ces résultats en dimension supérieure.

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

© 2010  Académie des sciences@@#104156@@
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