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1

2

$begingroup$

Let $Omega= B_1(0)$ the unit ball in $mathbb{R^2}$. How to prove that for $0<k<1/2$ the function $v(x)= |log(|x|)|^k$ is in

$$H^1(Omega)=left{ fin L^2(Omega) : frac{partial f}{partial x_i} in L^2(Omega) , i=1,2right}?$$

sobolev-spaces

share|cite|improve this question

edited Mar 13 at 16:58

Mars Plastic

1,485122

asked Mar 13 at 16:12

AnasAnas

254

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Welcome to stackexchange. What have you tried so far?
  $endgroup$
  – Mars Plastic
  Mar 13 at 16:17
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  First step first: did you show that $v in L^2(Omega)$?
  $endgroup$
  – Umberto P.
  Mar 13 at 17:48
  

  
  
  
  

add a comment | 

1

2

$begingroup$

Let $Omega= B_1(0)$ the unit ball in $mathbb{R^2}$. How to prove that for $0<k<1/2$ the function $v(x)= |log(|x|)|^k$ is in

$$H^1(Omega)=left{ fin L^2(Omega) : frac{partial f}{partial x_i} in L^2(Omega) , i=1,2right}?$$

sobolev-spaces

share|cite|improve this question

edited Mar 13 at 16:58

Mars Plastic

1,485122

asked Mar 13 at 16:12

AnasAnas

254

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Welcome to stackexchange. What have you tried so far?
  $endgroup$
  – Mars Plastic
  Mar 13 at 16:17
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  First step first: did you show that $v in L^2(Omega)$?
  $endgroup$
  – Umberto P.
  Mar 13 at 17:48
  

  
  
  
  

add a comment | 

$begingroup$

Let $Omega= B_1(0)$ the unit ball in $mathbb{R^2}$. How to prove that for $0<k<1/2$ the function $v(x)= |log(|x|)|^k$ is in

$$H^1(Omega)=left{ fin L^2(Omega) : frac{partial f}{partial x_i} in L^2(Omega) , i=1,2right}?$$

sobolev-spaces

share|cite|improve this question

edited Mar 13 at 16:58

Mars Plastic

1,485122

asked Mar 13 at 16:12

AnasAnas

254

$endgroup$

share|cite|improve this question

edited Mar 13 at 16:58

Mars Plastic

1,485122

asked Mar 13 at 16:12

AnasAnas

254

share|cite|improve this question

edited Mar 13 at 16:58

Mars Plastic

1,485122

asked Mar 13 at 16:12

AnasAnas

254

edited Mar 13 at 16:58

Mars Plastic

1,485122

edited Mar 13 at 16:58

Mars Plastic

1,485122

asked Mar 13 at 16:12

AnasAnas

254

asked Mar 13 at 16:12

AnasAnas

254