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Bounds for analtic functions

  1. May 13, 2010 #1
    1. The problem statement, all variables and given/known data

    Let u(x; y) be real, nonconstant, and continuous in a closed
    bounded region R. Let u(x; y) be harmonic in the interior of R. Prove that
    the maximum and minimum value of u(x; y) in this region occurs on the boundary.

    2. Relevant equations

    the theorem said that( a function analtic in bounded domain and continous up to and including its boundry attains its maximum modlus on the boundry

    3. The attempt at a solution

    can i suppose that u(x;y) is nonzero ?
  2. jcsd
  3. May 17, 2010 #2
    Is R connected?
    If so, this is just the maximum principle
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