## Deriving the expression of the Lorentz force using the language of a mathematician

This is a continuation of my previous “complaining” post on the language difference of mathematician vs physicists regarding the same thing.

## Random notes about physicists’ obsession with Einstein notations

I took a quantum physics class on Coursera this year and I found that the Mathematical language spoken by the two communities, math vs physics, are quite dif...

## Several explicit constructions of the Helmholtz decomposition

Here we present two approaches to construct Helmholtz decompositions.

## An identity for the continuous integral solution of the conservation law

This is an exercise in Evans, Partial Differential Equations (1st edition), page 164, problem 13.

## Kernels of a bounded operator’s extension

This is a post recording my answer to a question on Math StackExchange1 with some references in L. Tartar’s book2. https://math.stackexchange...

## Proof of the coercivity for Robin boundary problem

This is an exercise for finite element method most likely. Our question is:

## How to impose boundary condition for 2-dimensional curl-curl weak problem

First about the appropriate boundary condition we would like to impose: The cross product(scalar-$\mathrm{curl}$) in $\mathbb{R}^2$ is done by we embed a vec...

## An example on the limiting case of Sobolev embedding

Sobolev embedding When $p=n$