On geometric properties of harmonic Lip1-capacity
Pertti Mattila, Петр Владимирович Парамонов · Pacific Journal of Mathematics · 1995
We shall study geometric properties of the harmonic Lipjcapacity κ! n (E), E C R n . It is related to functions which are harmonic outside E and locally Lipschitzian everywhere. We shall show that κ! n+1 {E x /) is comparable to κ' n {E) for EcR n and for intervals / C R. We shall also show that if E lies on a Lipschitz graph, then κ' n (E) is comparable to the (nl)-dimensional Hausdorff measure Ή n ~1(E).Finally we give some general criteria to guarantee that κ! n {E) -0 although n n ~ι{E) >o.