PointwiseNorm.derivative

PointwiseNorm.derivative(self, vf)

Derivative of the point-wise norm operator at vf.

The derivative at F of the point-wise norm operator N with finite exponent p and weights w is the pointwise inner product with the vector field

x --> N(F)(x)^(1-p) * [ F_j(x) * |F_j(x)|^(p-2) ]_j

Note that this is not well-defined for F = 0. If p < 2, any zero component will result in a singularity.

Parameters

vfdomain element-like

Vector field F at which to evaluate the derivative.

Returns

derivPointwiseInner

Derivative operator at the given point vf.

Raises

NotImplementedError

• if the vector field space is complex, since the derivative is not linear in that case

• if the exponent is inf