Boundary Regularity for Functions in De Giorgi Classes

It is well-known that functions in De Giorgi classes are continuous up to the boundary, if this satisfies a geometric density condition, and the Dirichlet boundary datum is itself continuous. We give a new proof of this classical result relying on ideas that were originally proposed by Gariepy and Ziemer to prove the sufficient part of the Wiener criterion for the continuity of solutions to quasilinear elliptic equations of p -Laplace type.