Question

Under what conditions does $u$ with $supp(u) \subset \Omega$ belong to $H_0^1(\Omega)$?

score 70 · Answer 1 · 2026-04-12 02:34:01

70

Views

Under what conditions does $u$ with $supp(u) \subset \Omega$ belong to $H_0^1(\Omega)$?

Published on 12 Apr 2026 - 2:34

score 176 · Answer 2 · 2026-03-28 01:26:19

176

Views

Question concerning the proof of regularity for the Laplacian $f \in H^m(\Omega) \Rightarrow u \in H^{m+2}(\Omega) $

Published on 28 Mar 2026 - 1:26

score 45 · Answer 3 · 2026-04-11 21:39:03

45

Views

Is it true that $|∇u(x)|^2\chi_\Omega=|\nabla (u \chi_\Omega)|^2$

Published on 11 Apr 2026 - 21:39

score 874 · Answer 4 · 2026-04-13 16:33:07

874

Views

How to find out if a function belongs to $H^2$ or $H^1$

Published on 13 Apr 2026 - 16:33

score 784 · Answer 5 · 2026-03-26 02:47:49

784

Views

Morrey's inequality for Sobolev spaces of fractional order

Published on 26 Mar 2026 - 2:47

score 91 · Answer 6 · 2026-04-10 18:19:50

91

Views

Is tensor product of weighted Sobolev spaces dense?

Published on 10 Apr 2026 - 18:19

score 551 · Answer 7 · 2026-03-28 01:25:53

551

Views

Are weak (Sobolev) solutions to a linear ODE a classical ones?

Published on 28 Mar 2026 - 1:25

score 619 · Answer 8 · 2026-04-15 21:59:22

619

Views

Alexandrov Maximum Principle and $W^{2}_p$ estimates

Published on 15 Apr 2026 - 21:59

score 1.6k · Answer 9 · 2026-03-28 01:26:23

1.6k

Views

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

Published on 28 Mar 2026 - 1:26

score 238 · Answer 10 · 2026-03-28 01:25:59

238

Views

Passing from classical formulation to weak formulation for a general PDE

Published on 28 Mar 2026 - 1:25

score 66 · Answer 11 · 2026-04-16 06:11:17

66

Views

Find the Minimum of $ F(u)= \int\limits_{-2}^{+2}|u(x) - \chi_{[0,2]}(x)|dx + |Du|(\mathbb R)$.

Published on 16 Apr 2026 - 6:11

score 454 · Answer 12 · 2026-04-14 20:20:11

454

Views

Tensor product space dense in $H_0^1$?

Published on 14 Apr 2026 - 20:20

score 79 · Answer 13 · 2026-03-27 03:42:35

79

Views

Bound on Rayleigh quotient on $H^{1}_{\text{per}}[0,1]^{n}$

Published on 27 Mar 2026 - 3:42

score 141 · Answer 14 · 2026-04-16 08:25:02

141

Views

If $f$ satisfies $\int_{\Bbb{R}}\frac{f(x)\varphi(x)}{1+x^2}\,dx=0$ for some test functions $\varphi$, is $f$ zero?

Published on 16 Apr 2026 - 8:25

score 90 · Answer 15 · 2026-04-14 09:38:12

90

Views

What is assumed when one write "$\nabla f$" for $f\in L^p(\mathbb{R}^n)$?

Published on 14 Apr 2026 - 9:38

List Question

Under what conditions does $u$ with $supp(u) \subset \Omega$ belong to $H_0^1(\Omega)$?

Question concerning the proof of regularity for the Laplacian $f \in H^m(\Omega) \Rightarrow u \in H^{m+2}(\Omega) $

Is it true that $|∇u(x)|^2\chi_\Omega=|\nabla (u \chi_\Omega)|^2$

How to find out if a function belongs to $H^2$ or $H^1$

Morrey's inequality for Sobolev spaces of fractional order

Is tensor product of weighted Sobolev spaces dense?

Are weak (Sobolev) solutions to a linear ODE a classical ones?

Alexandrov Maximum Principle and $W^{2}_p$ estimates

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

Passing from classical formulation to weak formulation for a general PDE

Find the Minimum of $ F(u)= \int\limits_{-2}^{+2}|u(x) - \chi_{[0,2]}(x)|dx + |Du|(\mathbb R)$.

Tensor product space dense in $H_0^1$?

Bound on Rayleigh quotient on $H^{1}_{\text{per}}[0,1]^{n}$

If $f$ satisfies $\int_{\Bbb{R}}\frac{f(x)\varphi(x)}{1+x^2}\,dx=0$ for some test functions $\varphi$, is $f$ zero?

What is assumed when one write "$\nabla f$" for $f\in L^p(\mathbb{R}^n)$?

Trending Questions

Popular # Hahtags

Popular Questions