0
votes
1answer
30 views

Is $H_0^1$ something reasonable for the electric field for a perfect conductor?

I'm trying to pull over some concepts that were derived for Navier-Stokes like equations to Maxwell's equations for the perfect conductor. At a certain point, I am about to assume that the electric ...
4
votes
2answers
128 views

Twistor Function for Coulomb Field

In an article by Penrose in Hughston and Ward "Advances in Twistor Theory", it is claimed that the twistor function $$ f(Z^\alpha) = \log{\frac{Z^1Z^2 - Z^0Z^3}{Z^2Z^3}}$$ produces an anti-self-dual ...
0
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1answer
383 views

Proof of equality of the integral and differential form of Maxwell's equation

Just curious, can anyone show how the integral and differential form of Maxwell's equation is equivalent? (While it is conceptually obvious, I am thinking rigorous mathematical proof may be useful in ...
4
votes
4answers
652 views

How to interpret the continuity conditions in the PDEs (for example, Maxwell equations) originated in physics?

I am currently working on PDEs in physics, mostly Maxwell equations. I am a mathematics graduate student, and this question has been haunting me for years. In PDE theory, or more specifically the ...