Abstract and Applied Analysis

A New Extension of Serrin's Lower Semicontinuity Theorem

Xiaohong Hu and Shiqing Zhang

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Abstract

We present a new extension of Serrin's lower semicontinuity theorem. We prove that the variational functional f x , u , u d x defined on W l o c 1,1 is lower semicontinuous with respect to the strong convergence in L l o c 1 , under the assumptions that the integrand f x , s , ξ has the locally absolute continuity about the variable x .

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 368610, 7 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393444383

Digital Object Identifier
doi:10.1155/2013/368610

Mathematical Reviews number (MathSciNet)
MR3070186

Zentralblatt MATH identifier
1292.49016

Citation

Hu, Xiaohong; Zhang, Shiqing. A New Extension of Serrin's Lower Semicontinuity Theorem. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 368610, 7 pages. doi:10.1155/2013/368610. https://projecteuclid.org/euclid.aaa/1393444383


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