Data di Pubblicazione:
2008
Citazione:
The Ginzburg-Landau equation in the Heisenberg group / I. Birindelli, E. Valdinoci. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - 10:5(2008), pp. 671-719.
Abstract:
We consider a functional related with phase transition models in the Heisenberg group framework. We prove that level sets of local minimizers satisfy some density estimates, that is, they behave as "codimension one" sets. We thus deduce a uniform convergence property of these level sets to interfaces with minimal area. These results are then applied in the construction of (quasi)periodic, plane-like minimizers, i.e. minimizers of our functional whose level sets are contained in a spacial slab of universal size in a prescribed direction. As a limiting case, we obtain the existence of hypersurfaces contained in such a slab which minimize the surface area with respect to a given periodic metric.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Allen-Cahn-Ginzburg-Landau-type functionals; Geometric properties of minimizers; Subelliptic operators and minimal surfaces on the Heisenberg group
Elenco autori:
I. Birindelli, E. Valdinoci
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