Uniqueness for an Overdetermined Boundary Value Problem for p-Laplacian

摘要

For p > 1 set delta pu = div (inverted delta Up - 2 inverted delta u), and let mube a measure with compact support and absolutely continuous with respect to the p-capacity. Suppose for j = 1,2, there are functions Uj epsilon W 1,p and (bounded) domains Omega, both containing the support of mu and such that delta pUj = X