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Variational inequalities with one-sided irregular obstacles

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Abstract

The authors show that the Hölder continuity of the solutionu∈K≔{v∈H 1o (Ω) | v≤ψ in Ω} of the variational inequality

$$(\triangledown u,\triangledown u - \triangledown v) \leqslant (f,u - v),v\varepsilon \mathbb{K},$$

also holds under a one-sided Hölder condition on the obstacle ψ. This class of obstacles ψ contains the implicit obstacles of the quasivariational inequalities occuring in stochastic impulse control.

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Authors and Affiliations

  1. Institut für Angewandte Mathematik der Universität, Beringstraße 4-6, D-53, Bonn

    Jens Frehse

  2. Istituto Matematico, Università di Roma, I-00100, Roma

    Umberto Mosco

Authors
  1. Jens Frehse
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  2. Umberto Mosco
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Frehse, J., Mosco, U. Variational inequalities with one-sided irregular obstacles. Manuscripta Math 28, 219–233 (1979). https://doi.org/10.1007/BF01647973

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  • DOI: https://doi.org/10.1007/BF01647973

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