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Global gradient bounds for relaxed variational problems

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Abstract

We prove global Lipschitz regularity for solutionsu : Ω → ℝN of some relaxed variational problems in classes of functions with prescribed Dirichlet boundary data. The variational integrals under consideration are of the form ∫Ω W(▽ u )dx withW of quadratic growth.

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Authors and Affiliations

  1. Fachbereich 9 Mathematik, Universität des Saarlandes, 66123, Saarbrücken, Germany

    Martin Fuchs

  2. Young Scientists Lab. of Math. Physics, Chinese Academy of Sciences, P.O. Box 71007, 430071, Wuhan, P.R. of China

    Li Gongbao

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  1. Martin Fuchs
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  2. Li Gongbao
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Fuchs, M., Gongbao, L. Global gradient bounds for relaxed variational problems. Manuscripta Math 92, 287–302 (1997). https://doi.org/10.1007/BF02678195

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  • DOI: https://doi.org/10.1007/BF02678195

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