We continue the study of the space of functions with bounded fractional variation in of order introduced in our previous work (Comi and Stefani in J Funct Anal 277(10):3373-3435, 2019). After some technical improvements of certain results of Comi and Stefani (2019) which may be of some separated insterest, we deal with the asymptotic behavior of the fractional operators involved as . We prove that the -gradient of a -function converges in to the gradient for all as . Moreover, we prove that the fractional -variation converges to the standard De Giorgi's variation both pointwise and in the -limit sense as . Finally, we prove that the fractional -variation converges to the fractional -variation both pointwise and in the -limit sense as for any given .
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| http://dx.doi.org/10.1007/s13163-022-00429-y | DOI Listing |
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