Need hint: Gradient of function on boundary of a connected subset of $Bbb R^3$
Consider a scalar function $Bbb R^3toBbb R$ defined on a connected subset of $Bbb R^3$.
I want to calculate the direction of maximal increase for the entire domain:
On non-border parts of the domain this would be the gradient. However, I want the direction of maximal function value increase also on the border of the domain.
Is there a theory around this type of problem?
Thanks a lot in advance!
linear-algebra general-topology analysis manifolds
edited Dec 1 at 18:27
Tianlalu
3,12321038
asked Dec 1 at 17:57
jimmy_jammy
564
add a comment |
Consider a scalar function $Bbb R^3toBbb R$ defined on a connected subset of $Bbb R^3$.
I want to calculate the direction of maximal increase for the entire domain:
On non-border parts of the domain this would be the gradient. However, I want the direction of maximal function value increase also on the border of the domain.
Is there a theory around this type of problem?
Thanks a lot in advance!
linear-algebra general-topology analysis manifolds
edited Dec 1 at 18:27
Tianlalu
3,12321038
asked Dec 1 at 17:57
jimmy_jammy
564
add a comment |
Consider a scalar function $Bbb R^3toBbb R$ defined on a connected subset of $Bbb R^3$.
I want to calculate the direction of maximal increase for the entire domain:
On non-border parts of the domain this would be the gradient. However, I want the direction of maximal function value increase also on the border of the domain.
Is there a theory around this type of problem?
Thanks a lot in advance!
linear-algebra general-topology analysis manifolds
edited Dec 1 at 18:27
Tianlalu
3,12321038
asked Dec 1 at 17:57
jimmy_jammy
564
Consider a scalar function $Bbb R^3toBbb R$ defined on a connected subset of $Bbb R^3$.
I want to calculate the direction of maximal increase for the entire domain:
On non-border parts of the domain this would be the gradient. However, I want the direction of maximal function value increase also on the border of the domain.
Is there a theory around this type of problem?
Thanks a lot in advance!
linear-algebra general-topology analysis manifolds
linear-algebra general-topology analysis manifolds
edited Dec 1 at 18:27
Tianlalu
3,12321038
asked Dec 1 at 17:57
jimmy_jammy
564
edited Dec 1 at 18:27
Tianlalu
3,12321038
asked Dec 1 at 17:57
jimmy_jammy
564
edited Dec 1 at 18:27
Tianlalu
3,12321038
edited Dec 1 at 18:27
Tianlalu
3,12321038
edited Dec 1 at 18:27
Tianlalu
3,12321038
3,12321038
asked Dec 1 at 17:57
jimmy_jammy
564
asked Dec 1 at 17:57
jimmy_jammy
564
asked Dec 1 at 17:57
jimmy_jammy
564
564
add a comment |
add a comment |
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