Lösungen der poissongleichung und harmonische vektorfelder in unbeschränkten gebieten
J. Mäulen, Peter Christian Werner · Mathematical Methods in the Applied Sciences · 1983
Abstract In the first part of this paper we consider generalised solutions of the Poisson equation Δ U = F in open subsets of R n ( n ⩾ 3) with Dirichlet or Neumann boundary data. We prove existence and uniqueness theorems, not only for the corresponding interior and exterior problems, but also for domains with boundaries extending to infinity. In the second part we discuss generalised harmonic fields in open subsets of R 3 with vanishing Dirichlet or Neumann boundary condition.