Article

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


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
    6 0 0 0


Comptes Rendus Mathématique
Volume 335, n° 9
pages 733-738 (novembre 2002)
Doi : S1631-073X(02)02557-8
Received : 11 September 2002 ;  accepted : 13 September 2002
Classification et représentation probabiliste des solutions positives d'une équation elliptique semi-linéaire
Classification and probabilistic representation for the positive solutions of a semilinear elliptic equation
 

Benoit Mselati
Département de mathématiques et applications, École normale supérieure, 45, rue d'Ulm, 75230 Paris cedex 05, France 

Note présentée par Haïm Brézis

Résumé

Nous montrons que les solutions positives de Δu =u 2 dans un domaine lisse et borné de Rd sont uniquement caractérisées par leur trace fine au bord définie dans [6], répondant ainsi à une question ouverte importante de [2]. Une formule probabiliste faisant intervenir le serpent brownien et reliant une solution à sa trace fine est également obtenue. Nous prouvons en outre que toute solution est limite croissante de solutions majorées par des fonctions harmoniques dans D. Pour citer cet article : B. Mselati, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 733-738.

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

We prove that a nonnegative solution of Δu =u 2 in a bounded and smooth domain in Rd is uniquely determined by its fine trace on the boundary as defined in [6], thus answering a major open question of [2]. A probabilistic formula for a solution in terms of its fine trace and of the Brownian snake is also provided. Moreover, we show that every solution is the increasing limit of solutions which are dominated by a harmonic function in D. To cite this article: B. Mselati, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 733-738.

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


© 2002  Académie des sciences/Éditions scientifiques et médicales Elsevier SAS. All Rights Reserved.
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.
Close
Article Outline
You can move this window by clicking on the headline
@@#110903@@