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Gradient Continuity for Nonlinear Obstacle Problems

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Abstract

We prove that the gradients of solutions to obstacle problems are continuous if the gradients of obstacles satisfy a Dini type continuity assumption. We also consider coefficients and nonhomogeneous data and investigate their regularity conditions to obtain gradient continuity, extending to the constrained case results starting with those presented by Mingione (J Eur Math Soc 13:459–486, 2011).

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  1. School of Mathematics, Korea Institute for Advanced Study, Seoul, 02455, Korea

    Jihoon Ok

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  1. Jihoon Ok
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Ok, J. Gradient Continuity for Nonlinear Obstacle Problems. Mediterr. J. Math. 14, 16 (2017). https://doi.org/10.1007/s00009-016-0838-x

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  • DOI: https://doi.org/10.1007/s00009-016-0838-x

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