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Solving the Equation $\hbox{div}\, v = F\, \hbox{IN} {\cal C}_0(\open{R}^N, \open{R}^N)$
Published online by Cambridge University Press: 24 July 2018
Abstract
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 ∈ Ln(ℝn) and satisfying an estimate of the type ||v||∞ ⩽ C||f||n for any f ∈ Ln(ℝn), where C > 0 is related to the constant appearing in the Sobolev–Gagliardo–Nirenberg inequality for functions with bounded variation (BV functions).
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 61 , Issue 4 , November 2018 , pp. 1055 - 1061
- Copyright
- Copyright © Edinburgh Mathematical Society 2018