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Lösungen der poissongleichung und harmonische vektorfelder in unbeschränkten gebieten
Author(s) -
Mäulen J.,
Werner P.
Publication year - 1983
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670050117
Subject(s) - mathematics , neumann boundary condition , uniqueness , dirichlet boundary condition , mathematical analysis , dirichlet distribution , uniqueness theorem for poisson's equation , poisson's equation , boundary (topology) , pure mathematics , boundary value problem
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.