Article ID Journal Published Year Pages File Type
4668094 Advances in Mathematics 2007 20 Pages PDF
Abstract

This paper answers a question of Fuglede about minimal positive harmonic functions associated with irregular boundary points. As a consequence, an old and central problem of fine potential theory, concerning the Riesz decomposition, is resolved. Namely, it is shown that, on certain fine domains, there exist positive finely superharmonic functions which do not admit any positive finely harmonic minorant and yet are not fine potentials.

Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)