Non-linear balayage and applications

A theory of capacities has been extentively studied for Besov spaces [1]. H owever not much seems to have been done regarding non-linear potentials. We develop some of this here as consequences of the form of certain metric pr ojections. The non-linear potential theory is used to derive the form of tangent cones for a class of convex sets in Besov spaces. Tangent cones for obstacle pro blem arise when studying differentiability of metric projection. Characteri sing the tangent cones is the first step in these considerations. This has been done in some of the Sobolev spaces using Hilbert space methods. In thi s article we describe angent cones for obstacle problems precisely, using n on-linear potential theoretic ideas, for all Besov spaces B-alpha(p,q), 1 < p < infinity, 1 < q < infinity, alpha > 0.