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Questions on the calculus of variations, which deals with the optimization of functionals mostly defined on infinite dimensional spaces.
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Is every set with finite $\mathcal{H}^{n-1}$ measure a set of locally finite perimeter?
Given a measurable set $E \subset \mathbb{R}^d$, with $\mathcal{H}^{d-1} (\partial E) < +\infty$, is it true in general that $E$ is a set of locally finite perimeter? that is, is it true that $\int_B …
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A general rule for approximating the perimeter of a set with finite perimeter in terms of th...
I want to know if it is possible to have a general rule for approximating the perimeter of a set $E\subset \mathbb{R}^n$ with finite perimeter in terms of the volume (Lebesgue measure) of a sequence o …