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Compact Subdifferentials in Banach Spaces and Their Applications to Variational Functionals

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Abstract

We develop a theory of sublinear operators with compact values. Then, based on this theory, we construct a theory of first-order compact subdifferentials for maps in Banach spaces. The results are applicable to the calculation of compact subdifferentials of variational functionals with nonsmooth Lagrangians.

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Authors and Affiliations

  1. Vernadskii Tavria National University, Simferopol, Ukraine

    I. V. Orlov & Z. I. Khalilova

Authors
  1. I. V. Orlov
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  2. Z. I. Khalilova
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Correspondence to I. V. Orlov.

Additional information

Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 49, Proceedings of the Crimean Autumn Mathematical School-Symposium, 2013.

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Orlov, I.V., Khalilova, Z.I. Compact Subdifferentials in Banach Spaces and Their Applications to Variational Functionals. J Math Sci 211, 542–578 (2015). https://doi.org/10.1007/s10958-015-2617-9

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