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On the regularity of minimizers to degenerate functionals
On a 1-capacitary type problem in the plane
1. | Dipartimento di Matematica "U. Dini", Università di Firenze, viale Morgagni 67/A, I-50139 Firenze |
2. | Dip. Mat. “L. Tonelli”, Università di Pisa, L.go B. Pontecorvo 5, I-56127 Pisa, Italy |
3. | Dip. Matematica, Seconda Università di Napoli, V. Vivaldi 43, I-81100 Caserta, Italy |
  As a consequence of our result we determine the $1$-capacity of (a suitable representant of) sets with finite perimeter in the plane.
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Alessandro Ferriero, Nicola Fusco. A note on the convex hull of sets of finite perimeter in the plane. Discrete and Continuous Dynamical Systems - B, 2009, 11 (1) : 103-108. doi: 10.3934/dcdsb.2009.11.103 |
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Annalisa Cesaroni, Matteo Novaga. Volume constrained minimizers of the fractional perimeter with a potential energy. Discrete and Continuous Dynamical Systems - S, 2017, 10 (4) : 715-727. doi: 10.3934/dcdss.2017036 |
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Serena Dipierro, Alessio Figalli, Giampiero Palatucci, Enrico Valdinoci. Asymptotics of the $s$-perimeter as $s\searrow 0$. Discrete and Continuous Dynamical Systems, 2013, 33 (7) : 2777-2790. doi: 10.3934/dcds.2013.33.2777 |
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Kai Zehmisch. The codisc radius capacity. Electronic Research Announcements, 2013, 20: 77-96. doi: 10.3934/era.2013.20.77 |
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Benny Avelin, Tuomo Kuusi, Mikko Parviainen. Variational parabolic capacity. Discrete and Continuous Dynamical Systems, 2015, 35 (12) : 5665-5688. doi: 10.3934/dcds.2015.35.5665 |
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Lasse Kiviluoto, Patric R. J. Östergård, Vesa P. Vaskelainen. Sperner capacity of small digraphs. Advances in Mathematics of Communications, 2009, 3 (2) : 125-133. doi: 10.3934/amc.2009.3.125 |
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Chungen Liu, Qi Wang. Symmetrical symplectic capacity with applications. Discrete and Continuous Dynamical Systems, 2012, 32 (6) : 2253-2270. doi: 10.3934/dcds.2012.32.2253 |
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Samuel Amstutz, Antonio André Novotny, Nicolas Van Goethem. Minimal partitions and image classification using a gradient-free perimeter approximation. Inverse Problems and Imaging, 2014, 8 (2) : 361-387. doi: 10.3934/ipi.2014.8.361 |
[12] |
Gyula Csató. On the isoperimetric problem with perimeter density $r^p$. Communications on Pure and Applied Analysis, 2018, 17 (6) : 2729-2749. doi: 10.3934/cpaa.2018129 |
[13] |
Hayk Mikayelyan, Henrik Shahgholian. Convexity of the free boundary for an exterior free boundary problem involving the perimeter. Communications on Pure and Applied Analysis, 2013, 12 (3) : 1431-1443. doi: 10.3934/cpaa.2013.12.1431 |
[14] |
Antonio De Rosa, Domenico Angelo La Manna. A non local approximation of the Gaussian perimeter: Gamma convergence and Isoperimetric properties. Communications on Pure and Applied Analysis, 2021, 20 (5) : 2101-2116. doi: 10.3934/cpaa.2021059 |
[15] |
Tobias Sutter, David Sutter, John Lygeros. Capacity of random channels with large alphabets. Advances in Mathematics of Communications, 2017, 11 (4) : 813-835. doi: 10.3934/amc.2017060 |
[16] |
Jie Xiao. On the variational $p$-capacity problem in the plane. Communications on Pure and Applied Analysis, 2015, 14 (3) : 959-968. doi: 10.3934/cpaa.2015.14.959 |
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Adriano Festa, Simone Göttlich, Marion Pfirsching. A model for a network of conveyor belts with discontinuous speed and capacity. Networks and Heterogeneous Media, 2019, 14 (2) : 389-410. doi: 10.3934/nhm.2019016 |
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Jianbin Li, Ruina Yang, Niu Yu. Optimal capacity reservation policy on innovative product. Journal of Industrial and Management Optimization, 2013, 9 (4) : 799-825. doi: 10.3934/jimo.2013.9.799 |
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Qing Yang, Shiji Song, Cheng Wu. Inventory policies for a partially observed supply capacity model. Journal of Industrial and Management Optimization, 2013, 9 (1) : 13-30. doi: 10.3934/jimo.2013.9.13 |
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Yanjun He, Wei Zeng, Minghui Yu, Hongtao Zhou, Delie Ming. Incentives for production capacity improvement in construction supplier development. Journal of Industrial and Management Optimization, 2021, 17 (1) : 409-426. doi: 10.3934/jimo.2019118 |
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