All Questions

I wonder if there is any references for the study of the following type of spaces $$ X_{\delta,\alpha}=\{ u\in L^2_\delta(\mathbb{R}^n):\, u= (-\Delta)^\alpha f \quad\text{for some}\quad f\in L^2_{\...

In 1940 Sobolev recorded the following problem in the Scottish Book, and offered a bottle of wine for a solution. In 2015, when the second edition of the Scottish Book with updates and commentary on ...

On a bounded domain $\Omega \subset \mathbb R^d, d\geq 2$ with smooth boundary, it is well known that for the Dirichlet Laplacian $\Delta_D$, $D((-\Delta_D)^\frac12) = H^1_0(\Omega)$. I'm interested ...

Let $\Omega\subset\mathbb{R}^{n}$ be a open bounded set and $\partial\Omega$ be the boundary of $\Omega$. Following the reference text by Alois Kufner, Oldřich John and Svatopluk Fučík, Function ...

If $\Omega$ is an open Lipschitz domain with bounded boundary then their exists a continuous operator $E: W^{s,p}(\Omega) \rightarrow W^{s,p}(\mathbb{R}^d)$ where $s\in (0,1)$ such that $Eu=u$ on $\...