Skip to main content

All Questions

Filter by
Sorted by
Tagged with
-2 votes
2 answers
324 views

$f\in (W^{1,p}(\Omega)\cap C(\Omega) \cap L^{\infty}(\Omega))\setminus C(\bar{\Omega})$, $f=0$ on $\partial \Omega$ imply $f\in W^{1,p}_{0}(\Omega)$?

Q1: Let $p\geq 1$, and let $f\in W^{1,p}(\Omega)\cap C(\Omega)$. Assume also $f\in L^{\infty}(\Omega)$ and $f=0$ on $\partial \Omega$. Is it true that $f\in W^{1,p}_{0}(\Omega)$ even if $f\notin C(\...
Medo's user avatar
  • 852
-2 votes
1 answer
80 views

Density property for Sobolev spaces

My question is as follows: is the space $ C_c^{\infty}(\mathbb{R}^3 \setminus \mathcal{C}) $ dense in $ H^1( \mathbb{R}^3) $ where $ \mathcal{C} $ is the circle $ \{(x,y,z) \in \mathbb{R}^3 \mid x^2 +...
SemiMath's user avatar

1
10 11 12 13
14