On the Wiener Criterion and Quasilinear Obstacle Problems

Juha Heinonen, Tero Kilpelainen
1988 Transactions of the American Mathematical Society  
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