- #1
- 1,798
- 33
Hi,
I have the following problem, I have an electric field (which no charge) which satisfies the usual Laplace equation:
[tex]
\frac{\partial^{2}V}{\partial x^{2}}+\frac{\partial^{2}V}{\partial y^{2}}+\frac{\partial^{2}V}{\partial z^{2}}=0
[/tex]
in the region [itex]\mathbb{R}^{2}\times [\eta ,\infty ][/itex]. So basically it is the upper half z-plane where the boundary is some fixed surface [itex]\eta[/itex], I also know that on this surface:
[tex]
\frac{\partial V}{\partial x}=\frac{\partial\eta}{\partial x}
[/tex]
I can do this in 2D by the use of the Hilbert transform. Any suggestions?
I have the following problem, I have an electric field (which no charge) which satisfies the usual Laplace equation:
[tex]
\frac{\partial^{2}V}{\partial x^{2}}+\frac{\partial^{2}V}{\partial y^{2}}+\frac{\partial^{2}V}{\partial z^{2}}=0
[/tex]
in the region [itex]\mathbb{R}^{2}\times [\eta ,\infty ][/itex]. So basically it is the upper half z-plane where the boundary is some fixed surface [itex]\eta[/itex], I also know that on this surface:
[tex]
\frac{\partial V}{\partial x}=\frac{\partial\eta}{\partial x}
[/tex]
I can do this in 2D by the use of the Hilbert transform. Any suggestions?