math.AP

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

Embedding theorems for Weighted Sobolev Spaces
Last updated on 8 min read Expository

L. Craig Evans is a professor at UC Berkeley. For many students he is best known for his textbook on partial differential equations. I …
Last updated on 10 min read notes from talks

I try to reformulate an idea of Capoferri and Vassiliev in the infinitesimal limit and see where it goes.
Last updated on 5 min read research

As we all learned in a first course in PDEs, for "reasonable" initial data $u_0$, the solution to the linear heat equation …
Last updated on 4 min read mathematical diversions

The "Nirenberg trick" or "Nirenberg transformation" is the observation1 that the semilinear wave equation …
Last updated on 5 min read mathematical diversions

In this installment, we look at Schrödinger's equation with barriers, and study the decay of the solutions.
Last updated on 25 min read mathematical diversions

We use Laplace transform arguments to look at the convergence of infinite energy solutions of the free 1D Schrödinger's equation …
Last updated on 11 min read mathematical diversions

We look at the convergence of infinite energy solutions of the free 1D Schrödinger's equation to plane waves.
Last updated on 16 min read mathematical diversions

One of my current research interests is in the geometry of constant-mean-curvature time-like submanifolds of Minkowski space. A special …
Last updated on 8 min read mathematical diversions

Numpy simulation of how classical and quantum particles interact with potential barriers.
Last updated on 8 min read mathematical diversions