Show that f (x, y) = x2 ? y2 is harmonic. Verify the mea
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Show that f (x, y) = x2 ? y2 is harmonic. Verify the mean-value property for f (x, y) directly [expand f (a + r cos ?,b
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Show that f (x, y) = x2 ? y2 is harmonic. Verify the mean-value property for f (x, y) directly [expand f (a + r cos ?,b + r sin ? ) as a function of ? and compute I?(r)]. Show that x2 + y2 is not harmonic and does not satisfy the mean-value property.
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