ABSTRACT
Throughout this chapter, U denotes an open subset of Rn.
(i) A function f ∈ L1(U) has bounded variation in U if
sup
{∫ U
f div φdx ∣∣ φ ∈ C1c (U ;Rn), |φ| ≤ 1
} <∞.
We write BV (U)
to denote the space of functions of bounded variation in U . We do not identify two BV functions that agree Ln-a.e.
