Examples of Capacity for Some Elliptic Operators

Jang-Mei Wu
1992 Transactions of the American Mathematical Society  
We study L-capacities for uniformly elliptic operators of nondivergence form and construct examples of large sets having zero ¿-capacity for some L, and small sets having positive L-capacity. The relations between ellipticity constants of the coefficients and the sizes of these sets are also considered. A compact set S ç {|x| < 1} ç R" , n > 2, has zero capacity for the Laplacian if and only if it is a removable set for the class of bounded subharmonic functions on {|x| < 1}; equivalently,
more » ... exists a positive superharmonic function (^ +oo) on {|x| < 1}\S which approaches +oo continuously on S. In this note, we study L-capacities for uniformly elliptic operators of nondivergence form i,j J j J
doi:10.2307/2154115 fatcat:k42xgidvq5daxg2audqtjtzrdm