Research of the potential theory for elliptic type or parabolic type in unbounded domains and its consideration in stochastic analysis

点击翻译按钮获取中文摘要

Our aim was to research the potential theory for the elliptic type or the parabolic type in unbounded domains. In our study of the behavior of the solutions (harmonic functions) of the elliptic type differential equations i.e.Laplace equations in the neighbouhood of the point at infinity, we could consider qualitative properties and quantitative properties of thin sets on the complimentary sets of which the solutions behave very regularly. But the problems analogous to the solutions (temperatures) of the parabolic type differential equations i.e. heat equations could be almost unsolved except the problem about "the sets of determinations".