New posts in Sobolev Spaces

Must continuous $H^1(\mathbb{R}^2)$ function tend to zero at infinity?

Weak lower semicontinuity of functional with two arguments

A proof for $\nabla |u|^p = p\ \text{sgn}(u)|u|^{p-1}\nabla u$.

Weak solutions to $\Delta u=f$ are in $W^{2,2}$

What is the motivation of defining weak derivative as it is?

Convergence in $C([0,T_0],L^2)$ and uniform boundedness in $C([0,T_0],H^2)$ gives convergence in $C([0,T_0],H^1)$.

$L^1$ norm equivalent to weak topology of $W^{1,1}$?

Showing that Sobolev norms on manifolds are equivalent

Proof of Hardy inequality in $\mathbb{R}^n$

Intuition behind Sobolev Inequality