What is the definition of integrable tensor?
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I just googled 'integrable tensor' but I haven't found any stuff about it. I know this question is silly but the rigid definition is also important. Thanks in advance.
I saw this word here :
Definition Let $Omega$ be an open subset of $mathbbR^d$. A divergence-free positive symmetric tensor is a locally integrable tensor $x mapsto A(x)$ over $Omega$ with the properties that $A(x)in textSym_d^+$ almost everywhere, and $textDivA=0$.
My guess : Each entries of the tensor is integrable.
tensors integrable-systems
asked Sep 4 at 9:06
kayak
576318
add a comment |Â
up vote
0
down vote
favorite
I just googled 'integrable tensor' but I haven't found any stuff about it. I know this question is silly but the rigid definition is also important. Thanks in advance.
I saw this word here :
Definition Let $Omega$ be an open subset of $mathbbR^d$. A divergence-free positive symmetric tensor is a locally integrable tensor $x mapsto A(x)$ over $Omega$ with the properties that $A(x)in textSym_d^+$ almost everywhere, and $textDivA=0$.
My guess : Each entries of the tensor is integrable.
tensors integrable-systems
asked Sep 4 at 9:06
kayak
576318
Context helps, where did you see this expression ?
– Nicolas Hemelsoet
Sep 4 at 9:09
@NicolasHemelsoet Thanks for comment I put it in my question.
– kayak
Sep 4 at 9:16
1
I should think the definition pastes over from a locally integrable function,whereby a function is called locally integrable if, around every point in the domain, there is a neighborhood on which the function is integrable. I assume locally integrable tensors are broadly equivalent.
– Kevin
Sep 4 at 9:41
@Kevin Oh I thought so too. Could you write it down specifically? Then we all can see if we are thinking samely.
– kayak
Sep 4 at 9:43
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I just googled 'integrable tensor' but I haven't found any stuff about it. I know this question is silly but the rigid definition is also important. Thanks in advance.
I saw this word here :
Definition Let $Omega$ be an open subset of $mathbbR^d$. A divergence-free positive symmetric tensor is a locally integrable tensor $x mapsto A(x)$ over $Omega$ with the properties that $A(x)in textSym_d^+$ almost everywhere, and $textDivA=0$.
My guess : Each entries of the tensor is integrable.
tensors integrable-systems
asked Sep 4 at 9:06
kayak
576318
I just googled 'integrable tensor' but I haven't found any stuff about it. I know this question is silly but the rigid definition is also important. Thanks in advance.
I saw this word here :
Definition Let $Omega$ be an open subset of $mathbbR^d$. A divergence-free positive symmetric tensor is a locally integrable tensor $x mapsto A(x)$ over $Omega$ with the properties that $A(x)in textSym_d^+$ almost everywhere, and $textDivA=0$.
My guess : Each entries of the tensor is integrable.
tensors integrable-systems
tensors integrable-systems
asked Sep 4 at 9:06
kayak
576318
asked Sep 4 at 9:06
kayak
576318
edited Sep 4 at 9:15
asked Sep 4 at 9:06
kayak
576318
asked Sep 4 at 9:06
kayak
576318
asked Sep 4 at 9:06
kayak
576318
576318
Context helps, where did you see this expression ?
– Nicolas Hemelsoet
Sep 4 at 9:09
@NicolasHemelsoet Thanks for comment I put it in my question.
– kayak
Sep 4 at 9:16
1
I should think the definition pastes over from a locally integrable function,whereby a function is called locally integrable if, around every point in the domain, there is a neighborhood on which the function is integrable. I assume locally integrable tensors are broadly equivalent.
– Kevin
Sep 4 at 9:41
@Kevin Oh I thought so too. Could you write it down specifically? Then we all can see if we are thinking samely.
– kayak
Sep 4 at 9:43
add a comment |Â
Context helps, where did you see this expression ?
– Nicolas Hemelsoet
Sep 4 at 9:09
@NicolasHemelsoet Thanks for comment I put it in my question.
– kayak
Sep 4 at 9:16
1
I should think the definition pastes over from a locally integrable function,whereby a function is called locally integrable if, around every point in the domain, there is a neighborhood on which the function is integrable. I assume locally integrable tensors are broadly equivalent.
– Kevin
Sep 4 at 9:41
@Kevin Oh I thought so too. Could you write it down specifically? Then we all can see if we are thinking samely.
– kayak
Sep 4 at 9:43
Context helps, where did you see this expression ?
– Nicolas Hemelsoet
Sep 4 at 9:09
Context helps, where did you see this expression ?
– Nicolas Hemelsoet
Sep 4 at 9:09
@NicolasHemelsoet Thanks for comment I put it in my question.
– kayak
Sep 4 at 9:16
@NicolasHemelsoet Thanks for comment I put it in my question.
– kayak
Sep 4 at 9:16
1
1
I should think the definition pastes over from a locally integrable function,whereby a function is called locally integrable if, around every point in the domain, there is a neighborhood on which the function is integrable. I assume locally integrable tensors are broadly equivalent.
– Kevin
Sep 4 at 9:41
I should think the definition pastes over from a locally integrable function,whereby a function is called locally integrable if, around every point in the domain, there is a neighborhood on which the function is integrable. I assume locally integrable tensors are broadly equivalent.
– Kevin
Sep 4 at 9:41
@Kevin Oh I thought so too. Could you write it down specifically? Then we all can see if we are thinking samely.
– kayak
Sep 4 at 9:43
@Kevin Oh I thought so too. Could you write it down specifically? Then we all can see if we are thinking samely.
– kayak
Sep 4 at 9:43
add a comment |Â
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Context helps, where did you see this expression ?
– Nicolas Hemelsoet
Sep 4 at 9:09
@NicolasHemelsoet Thanks for comment I put it in my question.
– kayak
Sep 4 at 9:16
1
I should think the definition pastes over from a locally integrable function,whereby a function is called locally integrable if, around every point in the domain, there is a neighborhood on which the function is integrable. I assume locally integrable tensors are broadly equivalent.
– Kevin
Sep 4 at 9:41
@Kevin Oh I thought so too. Could you write it down specifically? Then we all can see if we are thinking samely.
– kayak
Sep 4 at 9:43