| Abstract: |
| About 15 years ago, Bourgain, Brezis and Mironescu proposed a new characterization of BV and W^(1,q) spaces (for q > 1) using a certain double integral functional involving radial mollifiers. We study what happens when one changes the power of |x-y| in the denominator of the integrand from q to 1. It turns out that for q > 1 the corresponding functionals see only the jumps of the BV-function. We further identify the function space relevant to the study of these functionals as an appropriate Besov space. We also present applications to the study of singular perturbation problems of Aviles-Giga type. |
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