ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

10. Partial Differential Equations

1991 MS Classification: 35XX, 49XX Sokolowski, Jan, Université Nancy 1, France Non–linear Balayage and Applications Some properties of non–linear potentials as consequences of the form of certain metric projections are developed. Non–negative potentials on R^{N} are potentials of non–negative Radon measures on R^{N}. We prove that capacity zero sets are subsets of poles of non–linear potentials, that the set of non–linear potentials while not necessarily convex is necessarily complete etc. Those are conterparts of results for Classical Potential theory. The non–linear potential theory is used to derive the form of tangent cones for a class of convex sets in Besov spaces B_{α}^{p,q}.