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Nondivergence elliptic and parabolic problems with irregular obstacles

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Abstract

We prove the natural weighted Calderón and Zygmund estimates for solutions to elliptic and parabolic obstacle problems in nondivergence form with discontinuous coefficients and irregular obstacles. We also obtain Morrey regularity results for the Hessian of the solutions and Hölder continuity of the gradient of the solutions.

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Authors and Affiliations

  1. Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul, 08826, Korea

    Sun-Sig Byun, Jehan Oh & Jinwan Park

  2. Department of Mathematical Sciences, Seoul National University, Seoul, 08826, Korea

    Ki-Ahm Lee

  3. Center for Mathematical Challenges, Korea Institute for Advanced Study, Seoul, 02455, Korea

    Ki-Ahm Lee

Authors
  1. Sun-Sig Byun
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  2. Ki-Ahm Lee
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  3. Jehan Oh
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  4. Jinwan Park
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Corresponding author

Correspondence to Jehan Oh.

Additional information

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea Government (NRF-2015R1A4A1041675).

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Byun, SS., Lee, KA., Oh, J. et al. Nondivergence elliptic and parabolic problems with irregular obstacles. Math. Z. 290, 973–990 (2018). https://doi.org/10.1007/s00209-018-2048-7

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