CAPACITY THEORY FOR MONOTONE-OPERATORS

If Au = -div(a(x, Du)) is a monotone operator defined on the Sobolev s pace W-l,W- p(R-n), l < p < +infinity, with a(x, 0) = 0 for a.e. x is an element of R-n, the capacity C-A(E, F) relative to A can be defined For every pair (E, F) of bounded sets in R-n with E subset of F. The main properties of the set function C-A(E, F) are investigated. In par ticular it is proved that C-A(E, F) is increasing and countably subadd itive with respect to E, decreasing with respect to F, and continuous, in a suitable sense, with respect to E and F.