How do you generalize the Laplace transform to more variables?

Question

Just what the title says. How can I take the Laplace transform of $f(x,y,z)$ ?

Answer 1

For multivariable version of Laplacian transformation, assume $t=(t_1,t_2,t_3)$, $X=(x,y,z)$, then $\mathcal L\{f(x,y,z)\}=\int e^{t\cdot X}f(X)$.