Lower Semicontinuity in of a Class of Functionals Defined on with Carathéodory Integrands

T. Wunderli

Abstract and Applied Analysis, 2021, vol. 2021, 1-6

Abstract:

We prove lower semicontinuity in for a class of functionals of the form where , is open and bounded, for each satisfies the linear growth condition and is convex in depending only on for a.e. Here, we recall for ; the gradient measure is decomposed into mutually singular measures and . As an example, we use this to prove that is lower semicontinuous in for any bounded continuous and any Under minor addtional assumptions on , we then have the existence of minimizers of functionals to variational problems of the form for the given due to the compactness of in

Date: 2021
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/AAA/2021/6709303.pdf (application/pdf)
http://downloads.hindawi.com/journals/AAA/2021/6709303.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:6709303

DOI: 10.1155/2021/6709303

Access Statistics for this article

More articles in Abstract and Applied Analysis from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().