# Tag Info

### A ball with slit at the radius is not $W^{1,1}$-extension domain

If $\Omega$ was a $W^{1,1}$-extension domain, then restrictions of $C_c^\infty(\mathbb{R}^n)$ functions to $\Omega$ would be dense in $W^{1,1}(\Omega)$ since they are dense in $W^{1,1}(\mathbb{R}^n)$. ...
• 1,808
1 vote
Accepted

### On the domain of the Neumann Laplacian

This is a partial (positive) answer for the convex case only but not every detail has been worked out. Let first $U$ be convex and smooth and all functions be in $C^3$ up to the boundary. Integrating ...
• 3,651

### Regularity of solution to Fokker Planck equation

A bootstrap argument is given in the proof of Lemma 10.7 of a paper of Mei-Montanari-Nguyen: https://web.stanford.edu/~montanar/RESEARCH/FILEPAP/mean_field.pdf The authors only show $C^{1,2}$ ...
• 1

### Second order differentiability of convex functions

The following argument is used in my recent paper with D. Azagra and A. Cappello (work in progress). The answer is yes. I asked about whether the proof of Theorem 1 can be modified so to cover Theorem ...
• 23.8k

### Is the measure density condition a necessary condition for bounding the Sobolev norm $W^{n,p}(\Omega)$ by the extremal terms?

No, the measure density condition is not necessary I would say. Possibly there are more precise arguments, but I would argue as follows, in a nutshell: The desired inequality can be proven using ...
• 1,808
1 vote
Accepted

• 2,240