REVIEW 1 cited by
On the gap between Gamma-limit and pointwise limit for a non-local approximation of the total variation
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
read the original abstract
We consider the approximation of the total variation of a function by the family of non-local and non-convex functionals introduced by H. Brezis and H.-M. Nguyen in a recent paper. The approximating functionals are defined through double integrals in which every pair of points contributes according to some interaction law. In this paper we answer two open questions concerning the dependence of the Gamma-limit on the interaction law. In the first result, we show that the Gamma-limit depends on the full shape of the interaction law, and not only on the values in a neighborhood of the origin. In the second result, we show that there do exist interaction laws for which the Gamma-limit coincides with the pointwise limit on smooth functions. The key argument is that for some special classes of interaction laws the computation of the Gamma-limit can be reduced to studying the asymptotic behavior of suitable multi-variable minimum problems.
Forward citations
Cited by 1 Pith paper
-
Exponential integrability in the spirit of Moser-Trudinger's inequalities of functions with finite non-local, non-convex energy
Functions with finite non-local energy I_{δ,p}(u,Ω) are exponentially integrable with exponent proportional to δ^{-1}, and the exponent p/d is shown to be sharp.
Discussion (0). Continue with ORCID to comment.