Abstract
Regularity for minimizers of the functional\(\mathop \smallint \limits_\Omega |\nabla v|\ln (1 + |\nabla v)dx\) on a set of vector-valued functions v: Ω⊂ taking prescribed values on the boundary ∂Ω is studied. It is shown that solutions of the dual variational problem belong to the class W 1 1,loc . In the case n′=2, higher integrability for minimizers of the direct variational problem is proved. Bibliography: 5 titles.
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Literature Cited
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Additional information
Dedicated to V. A. Solonnikov on his sixtieth anniversary
Published inZapiski Nauchnykh Seminarov POMI, Vol. 213, 1993, pp. 164–178.
Translated by G. A. Seregin
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Seregin, G.A. Some remarks on variational problems for functionals withLlnL growth. J Math Sci 84, 919–929 (1997). https://doi.org/10.1007/BF02399943
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DOI: https://doi.org/10.1007/BF02399943