2
votes
0answers
311 views

Nonlinear PDE and Green functions

This is somewhat of a curiosity that can hide somewhat deeper. For a Green function of a nonlinear PDE I mean something like $$ \partial^2\phi+V(\phi)=\delta^D(x). $$ I do not know if a real ...
2
votes
1answer
119 views

Distributional limits concerning the regularity of Maxwells equations

This question is related to my previous question about the regularity of the Maxwell equations. Assume we are working on a space where there are only electric point charges, $(q_i)$, and a blob of ...
0
votes
1answer
404 views

Calculating a distributional derivative

Suppose that we have a sequence of functions $u_j$ that are in $L^{\infty}(0,1)$. Then the sequence of maps $N_j(s) := \|u_j(s)\|^2$ are also in $L^{\infty}(0,1)$. Hence they give rise to ...
2
votes
1answer
852 views

A good reference for the wave front set

Hello, I am wondering whether anyone know some good references for the theory of wave front set, microlocal analysis? I have some basic knowledge of distribution theory at the level of the Rudin's ...