Asymptotic behavior of the $W^{1/q,q}$-norm of mollified $BV$ functions and applications to singular perturbation problems

Arkady Poliakovsky

Motivated by results of Figalli and Jerison and Hernández, we prove the following formula: \begin{equation*} \lim_{ε\to 0^+}\frac{1}{|\lnε|}\big\|η_ε*u\big\|^q_{W^{1/q,q}(Ω)}= C_0\…