# math.AP

This is an arXiv category tag for the analysis of partial differential equations.

### Notes on Sobolev Spaces

Lecture notes introducing Sobolev spaces.

### Mariş's Theorem

We describe a theorem due to Mihai Mariş concerning the symmetries of ground states.

### A Cute Little Wave Estimate

Let us consider first the linear wave equation $\Box u = 0$ on (1+d)-dimensional Minkowski space. A well known property of the wave …

### Skyrmions are narcissistic

Paper announcement and exposition.

### On the uniqueness of Kerr-Newman black holes

My PhD Thesis on characterization and conditional uniqueness of the Kerr-Newman solution in general relativity.