Optimal regularity for the fully nonlinear thin obstacle problem

  • Maria Colombo

    EPFL, Lausanne, Switzerland
  • Xavier Fernández-Real

    EPFL, Lausanne, Switzerland
  • Xavier Ros-Oton

    ICREA, Barcelona, Spain; Universitat de Barcelona, Barcelona, Spain; Centre de Recerca Matemàtica, Bellaterra, Spain
Optimal regularity for the fully nonlinear thin obstacle problem cover

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Abstract

In this work, we establish the optimal regularity for solutions to the fully nonlinear thin obstacle problem. In particular, we show the existence of an optimal exponent such that  is  on either side of the obstacle. In order to do that, we prove the uniqueness of blow-ups at regular points, as well as an expansion for the solution there. Finally, we also prove that if the operator is rotationally invariant, then and the solution is always .

Cite this article

Maria Colombo, Xavier Fernández-Real, Xavier Ros-Oton, Optimal regularity for the fully nonlinear thin obstacle problem. J. Eur. Math. Soc. (2024), published online first

DOI 10.4171/JEMS/1445