New posts in Sobolev Spaces

Gradient of Sobolev function on level sets

Does existence of the second weak derivative of $f\in L^2$ imply existence of the first?

Proving that the eigenfunctions of the Laplacian form a basis of $L^2(\Omega)$ (and of $H_0^1(\Omega)$)

Does there exist unique $u \in V$ satisfying integral equation?

If $u \in H^s(\mathbb{R}^n)$ for $s > n/2$, then $u \in L^\infty(\mathbb{R}^n)$?

Properties of function $f(x) = (1 + x^2)^{-\alpha/2}(\log(2+x^2))^{-1},\text{ }x \in \mathbb{R}$ with $0 < \alpha < 1$.

$W^{s,p}(\mathbb{R}^{n})$ Is Not Closed Under Multiplication when $s\leq n/p$

Significance of Sobolev spaces for numerical analysis & PDEs?

dual of $H^1_0$: $H^{-1}$ or $H_0^1$?

characterization of the dual space of the Sobolev space $H_0^1$