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

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  • T. Wunderli

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

Suggested Citation

  • T. Wunderli, 2021. "Lower Semicontinuity in of a Class of Functionals Defined on with Carathéodory Integrands," Abstract and Applied Analysis, Hindawi, vol. 2021, pages 1-6, November.
    • Handle: RePEc:hin:jnlaaa:6709303
    DOI: 10.1155/2021/6709303
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