The main result of this paper is a compactness property for sequences of liftings of Sobolev maps defined on an open bounded set Ω⊂Rn and taking values in the unit circle S1⊂R2. As a consequence, we prove that the problem of finding a lifting of a map, having the shortest jump set, has a solution. Next, we obtain two Γ-limits for sequences of Ambrosio-Tortorelli-type functionals on S1-valued maps, one of which turns out to be nonlocal, for topological reasons.
Bellettini, G., Marziani, R., Scala, R. (2027). On jump minimizing liftings for S1-valued maps and connections with Ambrosio-Tortorelli-type Γ-limits. JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES, 217 [10.1016/j.matpur.2026.103992].
On jump minimizing liftings for S1-valued maps and connections with Ambrosio-Tortorelli-type Γ-limits
Scala, Riccardo
2027-01-01
Abstract
The main result of this paper is a compactness property for sequences of liftings of Sobolev maps defined on an open bounded set Ω⊂Rn and taking values in the unit circle S1⊂R2. As a consequence, we prove that the problem of finding a lifting of a map, having the shortest jump set, has a solution. Next, we obtain two Γ-limits for sequences of Ambrosio-Tortorelli-type functionals on S1-valued maps, one of which turns out to be nonlocal, for topological reasons.
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https://hdl.handle.net/11365/1329395