H 1 ∩ L p versus C1 Local Minimizers
Author
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-6, 6 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-04-28
Country of Publication
Egypt
No. of Pages
6
Main Subjects
Abstract EN
We show that a local minimizer of Φ in the C1 topology must be a local minimizer in the H1∩Lp topology, under suitable assumptions for the functional Φ=(1/2)∫Ω|∇u|2+(1/p)∫Ω|u|p−∫ΩF(x,u) with supercritical exponent p>2∗=2n/(n−2).
This result can be used to establish a solution to the corresponding equation admitting sub- and supersolution.
Hence, we extend the conclusion proved by Brezis and Nirenberg (1993), the subcritical and critical case.
American Psychological Association (APA)
Zhong, Yansheng. 2014. H 1 ∩ L p versus C1 Local Minimizers. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-6.
https://search.emarefa.net/detail/BIM-1033908
Modern Language Association (MLA)
Zhong, Yansheng. H 1 ∩ L p versus C1 Local Minimizers. Abstract and Applied Analysis No. 2014 (2014), pp.1-6.
https://search.emarefa.net/detail/BIM-1033908
American Medical Association (AMA)
Zhong, Yansheng. H 1 ∩ L p versus C1 Local Minimizers. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-6.
https://search.emarefa.net/detail/BIM-1033908
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1033908