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P1) Prove the Mean Value Property in 2 dimensions: If u is harmonic in C R and D(xo, a) CN, then 1 u(xo) u(x)
P1) Prove the Mean Value Property in 2 dimensions: If u is harmonic in C R and D(xo, a) CN, then 1 u(xo) u(x) ds, 2 C(xo,a) where D(xo, a) = {x = R : |x xo| < a} and C(xo, a) = {x = R : |x x0| = a}, and integration on the circle is with respect to the arc length parametrization. Also show the MVP over the entire disk: u(xo) = 1 ) u(x) dx.
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Calculus Early Transcendentals
Authors: James Stewart
7th edition
538497904, 978-0538497909
