4 problems

Let $\Omega\subset\mathbb{R}^N$ be open and bounded with a $C^{1,1}$ boundary, let $p>1$ and $0<s<1$, and let $f\in L^q(\Omega)$. Let $u\in W^{s,p}_0(\Omega)$ solve the correspondi…

Local Hölder regularity conjecture. Then $u$ is locally Hölder continuous in $\Omega$.

Brasco's classification conjecture. All minimizers for $S_{s,p}$ are of the form

Let $u$ solve the fractional $p$-Laplacian evolution equation in a domain $\Omega$, with homogeneous Dirichlet data outside $\Omega$, and let…