AMBIENTUM BIOETHICA BIOLOGIA CHEMIA DIGITALIA DRAMATICA EDUCATIO ARTIS GYMNAST. ENGINEERING EPHEMERIDES EUROPAEA GEOGRAPHIA GEOLOGIA HISTORIA HISTORIA ARTIUM INFORMATICA IURISPRUDENTIA MATHEMATICA MUSICA NEGOTIA OECONOMICA PHILOLOGIA PHILOSOPHIA PHYSICA POLITICA PSYCHOLOGIA-PAEDAGOGIA SOCIOLOGIA THEOLOGIA CATHOLICA THEOLOGIA CATHOLICA LATIN THEOLOGIA GR.-CATH. VARAD THEOLOGIA ORTHODOXA THEOLOGIA REF. TRANSYLVAN
|
|||||||
The STUDIA UNIVERSITATIS BABEŞ-BOLYAI issue article summary The summary of the selected article appears at the bottom of the page. In order to get back to the contents of the issue this article belongs to you have to access the link from the title. In order to see all the articles of the archive which have as author/co-author one of the authors mentioned below, you have to access the link from the author's name. |
|||||||
STUDIA MATHEMATICA - Issue no. 1 / 2023 | |||||||
Article: |
GENERALIZED VERSUS CLASSICAL NORMAL DERIVATIVE. Authors: LUCAS FRESSE, VIORICA V. MOTREANU. |
||||||
Abstract: DOI: 10.24193/subbmath.2023.1.02 Published Online: 2023-03-20 Published Print: 2023-04-30 pp. 29-42 VIEW PDF FULL PDF Given a bounded domain with Lipschitz boundary, the general Green formula permits to justify that the weak solutions of a Neumann elliptic problem satisfy the Neumann boundary condition in a weak sense. The formula involves a generalized normal derivative. We prove a general result which establishes that the generalized normal derivative of an operator coincides with the classical one, provided that the operator is continuous. This result allows to deduce that, under usual regularity assumptions, the weak solutions of a Neumann problem satisfy the Neumann boundary condition in the classical sense. This information is necessary in particular for applying the strong maximum principle. Mathematics Subject Classification (2010): 26B20, 46E35, 46T20, 35J25, 35B50. Keywords: Lipschitz domain, normal derivative, Green formula, generalized normal derivative, Neumann problem, strong maximum principle.
|
|||||||