Solving the Equation $\hbox{div}\, v = F\, \hbox{IN} {\cal C}_0(\open{R}^N, \open{R}^N)$.

In the following note, we focus on the problem of existence of continuous solutions vanishing at infinity to the equation div v = f for f ∈ L ⁿ (ℝ ⁿ ) and satisfying an estimate of the type || v ||_∞ ⩽ C || f || _n for any f ∈ L ⁿ (ℝ ⁿ ), where C > 0 is related to the constant appearing in the Sobolev–Gagliardo–Nirenberg inequality for functions with bounded variation (BV functions). [ABSTRACT FROM AUTHOR]