# AIKAWA, Hiroaki:Department of Mathematics,Faculty of Science,Professor,Analysis

- Keyword(s):
- potential, harmonic
- Research Interest:
- Potential theory
- Research Activities:
- I have been studying potential theory. The main theme of potential
theory is the investigation of fundamental functions such as
(super)harmonic functions, subharmonic functions, plurisubharmonic
functions. The importance of the deep analysis of these functions has
been recognized as they play crucial roes in analysis, geometry,
probability, applied mathematics and so on. On the other hand, methods,
notions and aims of real and complex analysis, functional analysis and
probabilistic analysis have enriched potential theory.
Generally speaking, the interior properties of solutions to partial
differential equations have been exploited even though the equations are
complicated; if the domain is sufficiently smooth, the boundary behavior
of the solutions can be studied to some extent. Nevertheless the
boundary behavior of harmonic functions has many open problems if the
domain is not smooth. My research interest is "the boundary behavior"
of these functions in a wide sense. More specifically, I have been
studying the Fatou theorem, minimal fine topology, the integrability of
superharmonic functions, the additivity of capacity, the norm estimate
of the Green operator, Martin boundary and the boundary Harnack
principle.
- WebPage:
- http://www.math.sci.hokudai.ac.jp/~aik