Boundary regularity estimates in Hölder spaces with variable exponent

Abstract We present a general blow-up technique to obtain local regularity estimates for solutions, and their derivatives, of second order elliptic equations in divergence form Hölder spaces with variable exponent. The procedure allows extend the up portion boundary where Dirichlet or Neumann conditions are prescribed produces Schauder theory partial derivatives solutions any $$k\in {\mathbb {N}}$$ k ? N . strategy relies on construction class suitable regularizing problems an approximation argument. given data problem taken Lebesgue spaces, both