Boundary regularity for fully nonlinear integro-differential equations

  title={Boundary regularity for fully nonlinear integro-differential equations},
  author={Xavier Ros-Oton},
We study fine boundary regularity properties of solutions to fully nonlinear elliptic integro-differential equations of order 2s, with s 2 .0; 1/. We consider the class of nonlocal operators L L0, which consists of infinitesimal generators of stable Lévy processes belonging to the class L0 of Caffarelli–Silvestre. For fully nonlinear operators I elliptic with respect to L , we prove that solutions to IuD f in , uD 0 in R n , satisfy u=d s 2 C sC . N /, where d is the distance to @ and f 2 C… CONTINUE READING
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