The Lipschitz and harmonic capacities and in can be considered as high-dimensional versions of the so-called analytic and continuous analytic capacities and (resp.). In this article we provide a dual characterization of in the spirit of the classical one for the capacity by means of the Garabedian function. Using this new characterization, we show that for any compact set , where is the outer boundary of , and we solve an open problem posed by A. Volberg, which consists in estimating from below the Lipschitz harmonic capacity of a graph of a continuous function.
"A dual characterization of the harmonic capacity and applications." Duke Math. J. 153 (1) 1 - 22, 15 May 2010. https://doi.org/10.1215/00127094-2010-019