\[ \DeclareMathOperator{\dist}{dist} \]

Let \(f\in L^1_{\text{loc}}(\Omega)\) with \(\Omega\subset \mathbb{R}^n\) open. Then its mollification is defined by

\begin{equation*} f^{\varepsilon}=\eta_\varepsilon * f, \quad \text{in } \Omega_\varepsilon, \end{equation*}

where \(\Omega_\varepsilon=\{x\in \Omega \mid \dist(x, \partial U)>\varepsilon\}\subset \Omega\).

See also Link to heading

• standard mollifier