Does a Green function for the gradient exist? Specifically, consider the equation $$\vec{\nabla}_x\, G(\vec{x},\vec{x}') = \vec{\delta}(\vec{x}-\vec{x}'),$$ where $\vec{\delta}(\vec{x}-\vec{x}')$ is some sort of a vector generalization of the standard scalar delta function. Have such equations been investigated? If so, how does one derive the Green function for the gradient operator?
Asked
Active
Viewed 913 times