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Results tagged with laplace-equation
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user 108637
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Use stochastic process to express solution to Laplace equation in the whole space
If $f(x) / (1 + |x|)$ is integrable, then the solution $u$ is equal to the Newtonian potential of $f$:
$$ -u(x) = \frac{1}{4\pi} \int_{\mathbb R^3} \frac{f(y)}{|x - y|} \, dy . $$
And the Newtonian po …
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