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We study the Wiener criterion and variational inequalities with irregular obstacles for quasilinear elliptic operators A, A(x, Vu) ■ Vu £3 |Vu|p, in R". Local solutions are continuous at Wiener points of the obstacle function; if p > n -1, the converse is also shown to be true. If p > n -1, then a characterization of the thinness of a set at a point is given in terms of A-superharmonic functions.doi:10.2307/2001119 fatcat:o3c7vrstnnczlayga2wvixfaou