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Two-Phase Anisotropic Free Boundary Problems and Applications to the Bellman Equation in 2D

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Abstract

We prove Lipschitz continuity of solutions to a class of rather general two-phase anisotropic free boundary problems in 2D and we classify global solutions. As a consequence, we obtain \({C^{2,1}}\) regularity of solutions to the Bellman equation in 2D.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Texas at Austin, Austin, TX, 78712, USA

    L. Caffarelli

  2. Department of Mathematics, Barnard College, Columbia University, New York, NY, 10027, USA

    D. De Silva

  3. Department of Mathematics, Columbia University, New York, NY, 10027, USA

    O. Savin

Authors
  1. L. Caffarelli
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  2. D. De Silva
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  3. O. Savin
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Corresponding author

Correspondence to D. De Silva.

Additional information

Communicated by F. Lin

L. C. is supported by NSF Grant DMS-1500871. D. D. is supported by NSF Grant DMS-1301535. O. S. is supported by NSF Grant DMS-1200701.

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Caffarelli, L., De Silva, D. & Savin, O. Two-Phase Anisotropic Free Boundary Problems and Applications to the Bellman Equation in 2D. Arch Rational Mech Anal 228, 477–493 (2018). https://doi.org/10.1007/s00205-017-1198-9

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  • DOI: https://doi.org/10.1007/s00205-017-1198-9

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