List questions from sobolev-spaces | MathQa

Composite of a $\mathcal{C}^1$ real function and a $W^{1,p}$ function

Published on 02 Jan 2025 - 3:59

Extension theorem for Sobolev spaces $W^{1,\infty}(\Omega)$: is there an elementary proof?

Published on 12 Jan 2025 - 8:27

BMO space and log-lipschitz regularity

Published on 02 Jan 2025 - 3:37

Helmholtz Decomposition in Sobolev Space

Published on 26 Dec 2024 - 12:43

A question involving sharpening the bound on Sobolev type inequality with Sobolev spaces in terms of distributions of Schwartz functions

Published on 28 Dec 2024 - 9:34

Dirichlet eigenfunction cannot be extended to a continuous function on the closure

Published on 31 Dec 2024 - 12:22

If $\int_\Omega |\nabla (u-M)^+|^2 = 0$ where $u \in H^1(\Omega)$, and $u|_{\partial\Omega} \leq M$, does it follow that $u \leq M$ a.e?

Published on 26 Dec 2024 - 3:53

Some intuition on a specific problem on Sobolev's embedding theorem with its relation to Fourier transform of restricted functions

Published on 09 Jan 2025 - 20:33

Weak differentiability and diffeomorphisms

Published on 02 Jan 2025 - 21:50

Show that the functional $F(u)=\int ((u_x^2-1)^2+u_y^4)$ has zero infimum on a Sobolev space

Published on 02 Jan 2025 - 10:06