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Global regularity and stability of solutions to obstacle problems with nonstandard growth

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Abstract

We study the regularity properties of solutions to the single and double obstacle problem with non standard growth. Our main results are a global reverse Hölder inequality, Hölder continuity up to the boundary, and stability of solutions with respect to continuous perturbations in the variable growth exponent.

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Authors and Affiliations

  1. University of Verona, Strada le Grazie 15, 37134, Verona, Italy

    Michela Eleuteri

  2. Department of Mathematics, University of Turku, 20014, Turku, Finland

    Petteri Harjulehto

  3. Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35 (MaD), 40014, Jyväskylä, Finland

    Teemu Lukkari

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  1. Michela Eleuteri
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  2. Petteri Harjulehto
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  3. Teemu Lukkari
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Correspondence to Teemu Lukkari.

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Eleuteri, M., Harjulehto, P. & Lukkari, T. Global regularity and stability of solutions to obstacle problems with nonstandard growth. Rev Mat Complut 26, 147–181 (2013). https://doi.org/10.1007/s13163-011-0088-1

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