Jump detection in Besov spaces via a new BBM formula. Applications to Aviles-Giga type functionals

Arkady Poliakovsky

Motivated by the formula, due to Bourgain, Brezis and Mironescu, \begin{equation*} \lim_{\varepsilon\to 0^+} \int_Ω\int_Ω\frac{|u(x)-u(y)|^q}{|x-y|^q}\,ρ_\varepsilon(x-y)\,dx\,dy=K…