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Examples of Capacity for Some Elliptic Operators
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,
doi:10.2307/2154115
fatcat:k42xgidvq5daxg2audqtjtzrdm