March  2008, 3(1): 85-95. doi: 10.3934/nhm.2008.3.85

Leaf superposition property for integer rectifiable currents

1. 

Scuola Normale Superiore, p.za dei Cavalieri 7, Pisa, I-56126, Italy

2. 

Dipartimento di Matematica, Università degli Studi di Parma, viale G.P. Usberti 53/A (Campus), 43100 Parma, Italy

3. 

Laboratoire Jacques-Louis Lions & Centre National de la Recherche Scientique, Université Pierre et Marie Curie (Paris 6), 4 Place Jussieu, 75252 Paris, France

Received  June 2007 Revised  September 2007 Published  January 2008

We consider the class of integer rectifiable currents without boundary in $\R^n\times\R$ satisfying a positivity condition. We establish that these currents can be written as a linear superposition of graphs of finitely many functions with bounded variation.
Citation: Luigi Ambrosio, Gianluca Crippa, Philippe G. Lefloch. Leaf superposition property for integer rectifiable currents. Networks & Heterogeneous Media, 2008, 3 (1) : 85-95. doi: 10.3934/nhm.2008.3.85
[1]

Reuven Segev, Lior Falach. The co-divergence of vector valued currents. Discrete & Continuous Dynamical Systems - B, 2012, 17 (2) : 687-698. doi: 10.3934/dcdsb.2012.17.687

[2]

Roberta Ghezzi, Frédéric Jean. A new class of $(H^k,1)$-rectifiable subsets of metric spaces. Communications on Pure & Applied Analysis, 2013, 12 (2) : 881-898. doi: 10.3934/cpaa.2013.12.881

[3]

Shay Kels, Nira Dyn. Bernstein-type approximation of set-valued functions in the symmetric difference metric. Discrete & Continuous Dynamical Systems, 2014, 34 (3) : 1041-1060. doi: 10.3934/dcds.2014.34.1041

[4]

Mehmet Onur Fen, Marat Akhmet. Impulsive SICNNs with chaotic postsynaptic currents. Discrete & Continuous Dynamical Systems - B, 2016, 21 (4) : 1119-1148. doi: 10.3934/dcdsb.2016.21.1119

[5]

Didier Bresch, Jacques Simon. Western boundary currents versus vanishing depth. Discrete & Continuous Dynamical Systems - B, 2003, 3 (3) : 469-477. doi: 10.3934/dcdsb.2003.3.469

[6]

Vincenzo Recupero. Hysteresis operators in metric spaces. Discrete & Continuous Dynamical Systems - S, 2015, 8 (4) : 773-792. doi: 10.3934/dcdss.2015.8.773

[7]

Leandro M. Del Pezzo, Nicolás Frevenza, Julio D. Rossi. Convex and quasiconvex functions in metric graphs. Networks & Heterogeneous Media, 2021, 16 (4) : 591-607. doi: 10.3934/nhm.2021019

[8]

Jaeyoo Choy, Hahng-Yun Chu. On the dynamics of flows on compact metric spaces. Communications on Pure & Applied Analysis, 2010, 9 (1) : 103-108. doi: 10.3934/cpaa.2010.9.103

[9]

Rinaldo M. Colombo, Graziano Guerra. Differential equations in metric spaces with applications. Discrete & Continuous Dynamical Systems, 2009, 23 (3) : 733-753. doi: 10.3934/dcds.2009.23.733

[10]

Siegfried Carl, Christoph Tietz. Quasilinear elliptic equations with measures and multi-valued lower order terms. Discrete & Continuous Dynamical Systems - S, 2018, 11 (2) : 193-212. doi: 10.3934/dcdss.2018012

[11]

Peter Giesl. On a matrix-valued PDE characterizing a contraction metric for a periodic orbit. Discrete & Continuous Dynamical Systems - B, 2021, 26 (9) : 4839-4865. doi: 10.3934/dcdsb.2020315

[12]

Ugo Bessi. The stochastic value function in metric measure spaces. Discrete & Continuous Dynamical Systems, 2017, 37 (4) : 1819-1839. doi: 10.3934/dcds.2017076

[13]

Saul Mendoza-Palacios, Onésimo Hernández-Lerma. Stability of the replicator dynamics for games in metric spaces. Journal of Dynamics & Games, 2017, 4 (4) : 319-333. doi: 10.3934/jdg.2017017

[14]

Martin Bauer, Martins Bruveris, Philipp Harms, Peter W. Michor. Soliton solutions for the elastic metric on spaces of curves. Discrete & Continuous Dynamical Systems, 2018, 38 (3) : 1161-1185. doi: 10.3934/dcds.2018049

[15]

Thomas Lorenz. Mutational inclusions: Differential inclusions in metric spaces. Discrete & Continuous Dynamical Systems - B, 2010, 14 (2) : 629-654. doi: 10.3934/dcdsb.2010.14.629

[16]

Kazeem Olalekan Aremu, Chinedu Izuchukwu, Grace Nnenanya Ogwo, Oluwatosin Temitope Mewomo. Multi-step iterative algorithm for minimization and fixed point problems in p-uniformly convex metric spaces. Journal of Industrial & Management Optimization, 2021, 17 (4) : 2161-2180. doi: 10.3934/jimo.2020063

[17]

Simão P. S. Santos, Natália Martins, Delfim F. M. Torres. Noether currents for higher-order variational problems of Herglotz type with time delay. Discrete & Continuous Dynamical Systems - S, 2018, 11 (1) : 91-102. doi: 10.3934/dcdss.2018006

[18]

Hinke M. Osinga, Arthur Sherman, Krasimira Tsaneva-Atanasova. Cross-currents between biology and mathematics: The codimension of pseudo-plateau bursting. Discrete & Continuous Dynamical Systems, 2012, 32 (8) : 2853-2877. doi: 10.3934/dcds.2012.32.2853

[19]

Anton Petrunin. Harmonic functions on Alexandrov spaces and their applications. Electronic Research Announcements, 2003, 9: 135-141.

[20]

Feng Luo. Geodesic length functions and Teichmuller spaces. Electronic Research Announcements, 1996, 2: 34-41.

2020 Impact Factor: 1.213

Metrics

  • PDF downloads (44)
  • HTML views (0)
  • Cited by (0)

[Back to Top]