On Fine Limits and Curving-Shaped Limits

This paper studies the boundary behavior of the so-called SIH-functions, i.e., the functions satisfying the scale invariant Harnack inequality on a domain D R^N (N 2). Suppose that D contains a curving-cone at a point D and u is a SIH-function on D. Then u has a curving-shaped limit L at , if u has a -fine limit (especially, a p-fine limit in the sense of 6] or an -fine limit in the sense of the Riesz potential theory 4]) L at .AMS Subject Classification (2000): 31B25, 31C15, 30C65