REMOVABILITY OF SINGULARITIES IN POTENTIAL-THEORY

If Q is a compact metric space, L a system of its closed subsets and g : L --> R a prescribed nonnegative function, the conditions on g, L an d a closed F subset-of Q are specified guaranteeing the existence of a nontrivial Borel measure mu with support in F such that mu(L) less-th an-or-equal-to g(L), for-all L is-an-element-of L. For some kernels in potential theory these conditions permit to characterize geometricall y those sets which contain support of a nontrivial measure whose poten tial belongs to a given class of functions. Several applications conce rning removability of singularities of partial differential equations are presented.