Density in fractional Sobolev space
$begingroup$
Suppose $sin (0,1)$, $D$ is an open set in $mathbb{R}^d$. Define
$$
H^s=(1-Delta)^{-s/2} L^2(mathbb{R}^d),
$$
$$
H_D^s={fin H^s: f=0 a.e. on D^c}.
$$
Q: Is $C_c^infty(D)$ dense in $H_D^s$(with norm $|cdot|_{H^s}$) for any open set $D$?
Is there any element reference?
functional-analysis pde fractional-sobolev-spaces
asked Jan 23 at 19:45
Guohuan ZhaoGuohuan Zhao
283
$endgroup$
add a comment |
$begingroup$
Suppose $sin (0,1)$, $D$ is an open set in $mathbb{R}^d$. Define
$$
H^s=(1-Delta)^{-s/2} L^2(mathbb{R}^d),
$$
$$
H_D^s={fin H^s: f=0 a.e. on D^c}.
$$
Q: Is $C_c^infty(D)$ dense in $H_D^s$(with norm $|cdot|_{H^s}$) for any open set $D$?
Is there any element reference?
functional-analysis pde fractional-sobolev-spaces
asked Jan 23 at 19:45
Guohuan ZhaoGuohuan Zhao
283
$endgroup$
add a comment |
$begingroup$
Suppose $sin (0,1)$, $D$ is an open set in $mathbb{R}^d$. Define
$$
H^s=(1-Delta)^{-s/2} L^2(mathbb{R}^d),
$$
$$
H_D^s={fin H^s: f=0 a.e. on D^c}.
$$
Q: Is $C_c^infty(D)$ dense in $H_D^s$(with norm $|cdot|_{H^s}$) for any open set $D$?
Is there any element reference?
functional-analysis pde fractional-sobolev-spaces
asked Jan 23 at 19:45
Guohuan ZhaoGuohuan Zhao
283
$endgroup$
Suppose $sin (0,1)$, $D$ is an open set in $mathbb{R}^d$. Define
$$
H^s=(1-Delta)^{-s/2} L^2(mathbb{R}^d),
$$
$$
H_D^s={fin H^s: f=0 a.e. on D^c}.
$$
Q: Is $C_c^infty(D)$ dense in $H_D^s$(with norm $|cdot|_{H^s}$) for any open set $D$?
Is there any element reference?
functional-analysis pde fractional-sobolev-spaces
functional-analysis pde fractional-sobolev-spaces
asked Jan 23 at 19:45
Guohuan ZhaoGuohuan Zhao
283
asked Jan 23 at 19:45
Guohuan ZhaoGuohuan Zhao
283
asked Jan 23 at 19:45
Guohuan ZhaoGuohuan Zhao
283
asked Jan 23 at 19:45
Guohuan ZhaoGuohuan Zhao
283
asked Jan 23 at 19:45
Guohuan ZhaoGuohuan Zhao
283
283
add a comment |
add a comment |
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