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Total variation of a function

  1. Dec 12, 2011 #1
    Hello,

    I want to calculate the total variation [itex]\left \| f \right \|_{V(\Omega)}[/itex] with [itex]\Omega=(-1,1)[/itex] and [itex]f(x)=\mathrm{sgn}(x)[/itex].

    The total variation of a function is defined as follows:

    [itex] \left \| f \right \|_{V(\Omega)} :=\sup\left \{ \int_\Omega f\ \mathrm{div} (v)\ dx \ | \ v \in C^1_c(\Omega)^n \text{ with } \left \| v \right \|_{\infty,\Omega}\leq 1 \right \} [/itex]

    So, this is a very abstract definition and I don't know how to apply it...

    Can you please help me?

    Thank you in advance!

    Bye,
    Brian
     
  2. jcsd
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