American Institute of Mathematical Sciences

Advanced
June  2010, 28(2): 591-606. doi: 10.3934/dcds.2010.28.591

Sets with finite perimeter in Wiener spaces, perimeter measure and boundary rectifiability

Luigi Ambrosio 1, , Michele Miranda jr. 2, and  Diego Pallara 3,

1. 

Scuola Normale Superiore, p.za dei Cavalieri 7, Pisa, I-56126
2. 

Dipartimento di Matematica, Università di Ferrara, via Machiavelli 35, Ferrara, I-44121, Italy
3. 

Dipartimento di Matematica "Ennio De Giorgi”, Università del Salento, C.P. 193, Lecce, I-73100, Italy

Received  January 2010 Revised  April 2010 Published  April 2010

We discuss some recent developments of the theory of $BV$ functionsand sets of finite perimeter in infinite-dimensional Gaussianspaces. In this context the concepts of Hausdorff measure,approximate continuity, rectifiability have to be properlyunderstood. After recalling the known facts, we prove aSobolev-rectifiability result and we list some open problems.
Keywords: sets with finite perimeter, rectifiability., Wiener spaces.
Mathematics Subject Classification: Primary: 28C20, 49Q15, 26E15; Secondary: 60H0.
Citation: Luigi Ambrosio, Michele Miranda jr., Diego Pallara. Sets with finite perimeter in Wiener spaces, perimeter measure and boundary rectifiability. Discrete & Continuous Dynamical Systems, 2010, 28 (2) : 591-606. doi: 10.3934/dcds.2010.28.591
[1]

Alessandro Ferriero, Nicola Fusco. A note on the convex hull of sets of finite perimeter in the plane. Discrete & Continuous Dynamical Systems - B, 2009, 11 (1) : 103-108. doi: 10.3934/dcdsb.2009.11.103
[2]

Xing Wang, Chang-Qi Tao, Guo-Ji Tang. Differential optimization in finite-dimensional spaces. Journal of Industrial & Management Optimization, 2016, 12 (4) : 1495-1505. doi: 10.3934/jimo.2016.12.1495
[3]

Linda Beukemann, Klaus Metsch, Leo Storme. On weighted minihypers in finite projective spaces of square order. Advances in Mathematics of Communications, 2015, 9 (3) : 291-309. doi: 10.3934/amc.2015.9.291
[4]

Alexander A. Davydov, Massimo Giulietti, Stefano Marcugini, Fernanda Pambianco. Linear nonbinary covering codes and saturating sets in projective spaces. Advances in Mathematics of Communications, 2011, 5 (1) : 119-147. doi: 10.3934/amc.2011.5.119
[5]

Steve Hofmann, Dorina Mitrea, Marius Mitrea, Andrew J. Morris. Square function estimates in spaces of homogeneous type and on uniformly rectifiable Euclidean sets. Electronic Research Announcements, 2014, 21: 8-18. doi: 10.3934/era.2014.21.8
[6]

Jeong-Yup Lee, Boris Solomyak. On substitution tilings and Delone sets without finite local complexity. Discrete & Continuous Dynamical Systems, 2019, 39 (6) : 3149-3177. doi: 10.3934/dcds.2019130
[7]

Natalie Priebe Frank, Lorenzo Sadun. Topology of some tiling spaces without finite local complexity. Discrete & Continuous Dynamical Systems, 2009, 23 (3) : 847-865. doi: 10.3934/dcds.2009.23.847
[8]

Piotr Gwiazda, Piotr Orlinski, Agnieszka Ulikowska. Finite range method of approximation for balance laws in measure spaces. Kinetic & Related Models, 2017, 10 (3) : 669-688. doi: 10.3934/krm.2017027
[9]

Angela Aguglia, Antonio Cossidente, Giuseppe Marino, Francesco Pavese, Alessandro Siciliano. Orbit codes from forms on vector spaces over a finite field. Advances in Mathematics of Communications, 2020  doi: 10.3934/amc.2020105
[10]

Harald Fripertinger. The number of invariant subspaces under a linear operator on finite vector spaces. Advances in Mathematics of Communications, 2011, 5 (2) : 407-416. doi: 10.3934/amc.2011.5.407
[11]

Sophie Guillaume. Evolution equations governed by the subdifferential of a convex composite function in finite dimensional spaces. Discrete & Continuous Dynamical Systems, 1996, 2 (1) : 23-52. doi: 10.3934/dcds.1996.2.23
[12]

Gabriel Fuhrmann, Jing Wang. Rectifiability of a class of invariant measures with one non-vanishing Lyapunov exponent. Discrete & Continuous Dynamical Systems, 2017, 37 (11) : 5747-5761. doi: 10.3934/dcds.2017249
[13]

Klaus Metsch. A note on Erdős-Ko-Rado sets of generators in Hermitian polar spaces. Advances in Mathematics of Communications, 2016, 10 (3) : 541-545. doi: 10.3934/amc.2016024
[14]

Liangwei Wang, Jingxue Yin, Chunhua Jin. $\omega$-limit sets for porous medium equation with initial data in some weighted spaces. Discrete & Continuous Dynamical Systems - B, 2013, 18 (1) : 223-236. doi: 10.3934/dcdsb.2013.18.223
[15]

Annibale Magni, Matteo Novaga. A note on non lower semicontinuous perimeter functionals on partitions. Networks & Heterogeneous Media, 2016, 11 (3) : 501-508. doi: 10.3934/nhm.2016006
[16]

Annalisa Cesaroni, Matteo Novaga. Volume constrained minimizers of the fractional perimeter with a potential energy. Discrete & Continuous Dynamical Systems - S, 2017, 10 (4) : 715-727. doi: 10.3934/dcdss.2017036
[17]

Serena Dipierro, Alessio Figalli, Giampiero Palatucci, Enrico Valdinoci. Asymptotics of the $s$-perimeter as $s\searrow 0$. Discrete & Continuous Dynamical Systems, 2013, 33 (7) : 2777-2790. doi: 10.3934/dcds.2013.33.2777
[18]

Peter Müller, Gábor P. Nagy. On the non-existence of sharply transitive sets of permutations in certain finite permutation groups. Advances in Mathematics of Communications, 2011, 5 (2) : 303-308. doi: 10.3934/amc.2011.5.303
[19]

Farzane Amirzade, Mohammad-Reza Sadeghi, Daniel Panario. QC-LDPC construction free of small size elementary trapping sets based on multiplicative subgroups of a finite field. Advances in Mathematics of Communications, 2020, 14 (3) : 397-411. doi: 10.3934/amc.2020062
[20]

Tanja Eisner, Pavel Zorin-Kranich. Uniformity in the Wiener-Wintner theorem for nilsequences. Discrete & Continuous Dynamical Systems, 2013, 33 (8) : 3497-3516. doi: 10.3934/dcds.2013.33.3497

2019 Impact Factor: 1.338

Tools

Metrics

  • PDF downloads (56)
  • HTML views (0)
  • Cited by (7)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences