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Existence of localizable solutions to nonlinear parabolic problems with irregular obstacles

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Abstract

We introduce the concept of localizable solutions of parabolic obstacle problems of p-Laplace-type with highly irregular obstacles and provide corresponding existence results. The main new feature of the constructed solutions is that they solve the problem locally, which is the appropriate notion for the examination of local properties like regularity. As an application, we derive Calderón–Zygmund estimates for the spatial gradient of localizable solutions to parabolic obstacle problems.

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  1. Faculty of Mathematics, University Duisburg-Essen, D-45117, Essen, Germany

    Christoph Scheven

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  1. Christoph Scheven
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Scheven, C. Existence of localizable solutions to nonlinear parabolic problems with irregular obstacles. manuscripta math. 146, 7–63 (2015). https://doi.org/10.1007/s00229-014-0684-8

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  • DOI: https://doi.org/10.1007/s00229-014-0684-8

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