Show that u(x, y) = y/π ∫-∞∞ f(t) dt / ((x - t)2+y2) satisfies uxx + uyy = 0.
The Attempt at a Solution
I'm not even sure Leibniz' Rule can be applied here since there seems to be a discontinuity in the integrand when x=t and y=0. When I use it and take the second derivatives, I get terms that have no way of cancelling (for example the -2(x-t) and -2y terms). I also tried integration by parts first but it did not simplify things.