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2013 A New Extension of Serrin's Lower Semicontinuity Theorem
Xiaohong Hu, Shiqing Zhang
Abstr. Appl. Anal. 2013(SI01): 1-7 (2013). DOI: 10.1155/2013/368610

Abstract

We present a new extension of Serrin's lower semicontinuity theorem. We prove that the variational functional${\int }_{\mathrm{\Omega}}^{}f(x,u,{u}^{\prime })dx$ defined on ${W}_{loc}^{1,1}(\mathrm{\Omega})$ is lower semicontinuous with respect to the strong convergence in ${L}_{loc}^{1}$, under the assumptions that the integrand $f(x,s,\xi )$ has the locally absolute continuity about the variable $x$.

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Xiaohong Hu. Shiqing Zhang. "A New Extension of Serrin's Lower Semicontinuity Theorem." Abstr. Appl. Anal. 2013 (SI01) 1 - 7, 2013. https://doi.org/10.1155/2013/368610

Information

Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 1292.49016
MathSciNet: MR3070186
Digital Object Identifier: 10.1155/2013/368610

Rights: Copyright © 2013 Hindawi

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