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Green's function and Dirichlet boundary problem

  1. May 5, 2010 #1
    Is it true that there always exists Green's function for Dirichlet boundary problem.
    I mean a function G(r,r') which fullfils the following conditions:
    [tex] div (\epsilon grad G(r,r')) =- \delta(r,r')[/tex] inside volume V and G(r,r') is 0 on
    boundary of V. If V is whole space there exists obvious solution (Coulomb potential)
    but I wonder if there exists solution for all V.
  2. jcsd
  3. May 5, 2010 #2


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    Science Advisor

    G is the potential of a point charge in a volume bounded by a grounded surface.
    This always exists.
  4. May 5, 2010 #3
    Yes, you are right but only when the situation is physically realizable.
    What is the answer for mathematical problem describe above
    (we have only one differential equation + boundary condition,
    without any physics behind)?
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