Minimizers for nonlocal perimeters of Minkowski type |
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Authors: | Annalisa?Cesaroni Serena?Dipierro Email author" target="_blank">Matteo?NovagaEmail author Enrico?Valdinoci |
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Institution: | 1.Dipartimento di Scienze Statistiche,Università di Padova,Padua,Italy;2.Dipartimento di Matematica,Università di Milano,Milan,Italy;3.Dipartimento di Matematica,Università di Pisa,Pisa,Italy;4.School of Mathematics and Statistics,University of Melbourne,Parkville,Australia;5.IMATI-CNR,Pavia,Italy |
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Abstract: | We study a nonlocal perimeter functional inspired by the Minkowski content, whose main feature is that it interpolates between the classical perimeter and the volume functional. This nonlocal functionals arise in concrete applications, since the nonlocal character of the problems and the different behaviors of the energy at different scales allow the preservation of details and irregularities of the image in the process of removing white noises, thus improving the quality of the image without losing relevant features. In this paper, we provide a series of results concerning existence, rigidity and classification of minimizers, compactness results, isoperimetric inequalities, Poincaré–Wirtinger inequalities and density estimates. Furthermore, we provide the construction of planelike minimizers for this generalized perimeter under a small and periodic volume perturbation. |
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