標題: On a problem of Dynkin
作者: Sheu, YC
應用數學系
Department of Applied Mathematics
關鍵字: superdiffusion;graph of superdiffusion;semilinear partial differential equation;G-polarity;H-polarity;Hausdorff dimension;box dimension;restricted Hausdorff dimension
公開日期: 1-十二月-1999
摘要: Consider an (L, alpha)-superdiffusion X on R-d, where L is an uniformly elliptic differential operator in R-d, and 1 < alpha less than or equal to 2. The G-polar sets for X are subsets of R x R-d which have no intersection with the graph G of X, and they are related to the removable singularities for a corresponding nonlinear parabolic partial differential equation. Dynkin characterized the G-polarity of a general analytic set A subset of R x R-d in term of the Bessel capacity of A, and Sheu in term of the restricted Hausdorff dimension. In this paper we study in particular the G-polarity of sets of the form E x F, where E and F are two Borel subsets of R and R-d respectively. We establish a relationship between the restricted Hausdorff dimension of E x F and the usual Hausdorff dimensions of E and F. As an application, we obtain a criterion for G-polarity of E x F in terms of the Hausdorff dimensions of E and F, which also gives an answer to a problem proposed by Dynkin in the 1991 Wald Memorial Lectures.
URI: http://hdl.handle.net/11536/30949
ISSN: 0002-9939
期刊: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
Volume: 127
Issue: 12
起始頁: 3721
結束頁: 3728
顯示於類別:期刊論文


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