Editing Bounded variation (section)

===Research works===
*{{Citation
 | last1 =Ambrosio
 | first1 =Luigi
 | author-link =Luigi Ambrosio
 | last2 =Fusco
 | first2 =Nicola
 | author2-link =Nicola Fusco
 | last3 =Pallara
 | first3 =Diego
 | title =Functions of bounded variation and free discontinuity problems
 | place =Oxford
 | publisher =The Clarendon Press / Oxford University Press
 | series =Oxford Mathematical Monographs
 | year =2000
 | pages =xviii+434
 | isbn =978-0-19-850245-6
 | mr =1857292
 | zbl =0957.49001
}}. 
*{{Citation
 | last =Brudnyi
 | first =Yuri
 | author-link =Yuri Brudnyi
 | editor-last =Randrianantoanina
 | editor-first =Beata
 | editor2-last =Randrianantoanina
 | editor2-first =Narcisse
 | contribution =Multivariate functions of bounded {{math|(''k'', ''p'')}}–variation
 | contribution-url =https://www.degruyter.com/view/books/9783110918298/9783110918298.37/9783110918298.37.xml
 | title =Banach Spaces and their Applications in Analysis. Proceedings of the international conference, Miami University, Oxford, OH, USA, May 22--27, 2006. In honor of Nigel Kalton's 60th birthday
 | place =Berlin–Boston
 | publisher =Walter De Gruyter
 | year =2007
 | pages =37–58
 | doi =10.1515/9783110918298.37
 | isbn =978-3-11-019449-4
 | mr =2374699
 | zbl = 1138.46019
| doi-access =
 }}
*{{Citation
| last1 =  Dunford
| first1 = Nelson
| author-link = Nelson Dunford
| last2 = Schwartz
| first2 = Jacob T.
| author2-link = Jacob T. Schwartz
| title = Linear operators. Part I: General Theory
| place = New York–London–Sydney
| publisher = Wiley-Interscience
| year = 1958
| series = Pure and Applied Mathematics
| volume = VII
| isbn = 0-471-60848-3
| zbl =  0084.10402
}}. Includes a discussion of the functional-analytic properties of spaces of functions of bounded variation.
*{{Citation
| last1 = Giaquinta
| first1 = Mariano
| author-link = Mariano Giaquinta
| last2 = Modica
| first2 = Giuseppe
| last3 = Souček
| first3 = Jiří
| title = Cartesian Currents in the Calculus of Variation I
| place = Berlin-Heidelberg-New York
| publisher = Springer Verlag
| year = 1998
| series = [[Ergebnisse der Mathematik und ihrer Grenzgebiete]]. 3. Folge. A Series of Modern Surveys in Mathematics
| volume = 37
| url = https://books.google.com/books?id=xx2vhd_uPS0C
| isbn = 3-540-64009-6
| zbl = 0914.49001}}.
*{{Citation
| last = Giusti
| first = Enrico
| author-link = Enrico Giusti
| title = Minimal surfaces and functions of bounded variations
| place = Basel–Boston–Stuttgart
| publisher = Birkhäuser Verlag
| year = 1984
| series = Monographs in Mathematics
| volume = 80
| url = https://books.google.com/books?id=dNgsmArDoeQC
| pages=XII+240
| isbn = 978-0-8176-3153-6
| mr=775682 
| zbl =0545.49018}}, particularly part I, chapter 1 "''Functions of bounded variation and Caccioppoli sets''". A good reference on the theory of [[Caccioppoli set]]s and their application to the [[minimal surface]] problem.
*{{Citation
| last = Halmos
| first = Paul
| author-link = Paul Halmos
| title = Measure theory
| publisher = Van Nostrand and Co.
| year = 1950
| url = https://books.google.com/books?id=-Rz7q4jikxUC
| isbn = 978-0-387-90088-9
| zbl = 0040.16802
}}. The link is to a preview of a later reprint by Springer-Verlag.
*{{Citation
| last1 = Hudjaev
| first1 = Sergei Ivanovich 
| last2 = Vol'pert
| first2 = Aizik Isaakovich
| author2-link = Aizik Isaakovich Vol'pert
| title = Analysis in classes of discontinuous functions and equations of mathematical physics
| place = Dordrecht–Boston–Lancaster
| publisher = Martinus Nijhoff Publishers
| year = 1985
| series = Mechanics: analysis
| volume = 8
| url = https://books.google.com/books?id=lAN0b0-1LIYC
| mr = 785938 
| isbn = 90-247-3109-7
| zbl = 0564.46025
}}. The whole book is devoted to the theory of {{math|BV}} functions and their applications to problems in [[mathematical physics]] involving [[discontinuous function]]s and geometric objects with [[smooth function|non-smooth]] [[boundary (topology)|boundaries]].
*{{Citation
| last1 = Kannan
| first1 = Rangachary
| last2 = Krueger
| first2 = Carole King
| title = Advanced analysis on the real line
| place = Berlin–Heidelberg–New York
| publisher = Springer Verlag
| year = 1996
| series = Universitext
| pages = x+259
| isbn = 978-0-387-94642-9
| mr = 1390758
| zbl = 0855.26001
}}. Maybe the most complete book reference for the theory of {{math|BV}} functions in one variable: classical results and advanced results are collected in chapter 6 "''Bounded variation''" along with several exercises. The first author was a collaborator of [[Lamberto Cesari]].
*{{Citation
| first1=Andrej N.
| last1=Kolmogorov
| author-link= Andrey Kolmogorov
| first2=Sergej V.
| last2=Fomin
| author2-link=Sergei Fomin
| title=Introductory Real Analysis
| publisher=Dover Publications
| pages=xii+403
| url=https://books.google.com/books?id=z8IaHgZ9PwQC
| place=New York
| year=1969
| isbn = 0-486-61226-0
| mr=0377445 
| zbl=0213.07305
}}.
*{{Citation
 | last =Leoni
 | first =Giovanni
 | title = A First Course in Sobolev Spaces
 | edition = Second
 | publisher =American Mathematical Society
 | series = Graduate Studies in Mathematics
 | year =2017
 | pages =xxii+734
 | isbn = 978-1-4704-2921-8
 }}. 
*{{Citation
| last1 = Màlek
| first1 = Josef
| last2 = Nečas
| first2 = Jindřich
| last3 = Rokyta
| first3 = Mirko
| last4 = Růžička
| first4 = Michael
| title = Weak and measure-valued solutions to evolutionary PDEs
| place = London–Weinheim–New York–Tokyo–Melbourne–Madras
| publisher = Chapman & Hall CRC Press
| year = 1996
| series = Applied Mathematics and Mathematical Computation
| volume = 13
| pages = xi+331
| url = https://books.google.com/books?id=30_PBBzwSfAC
| isbn = 0-412-57750-X
| mr = 1409366
| zbl = 0851.35002}}. One of the most complete monographs on the theory of [[Young measure]]s, strongly oriented to applications in continuum mechanics of fluids.
*{{Citation
| last = Maz'ya
| first = Vladimir G.
| author-link = Vladimir Gilelevich Maz'ya
| title = Sobolev Spaces
| publisher = Springer-Verlag
| location = Berlin–Heidelberg–New York
| year = 1985
| isbn=0-387-13589-8
| zbl = 0692.46023
}}; particularly chapter 6, "On functions in the space {{math|BV(Ω)}}". One of the best monographs on the theory of [[Sobolev space]]s.
*{{Citation
| first = Jean Jacques
| last = Moreau
| author-link = Jean-Jacques Moreau
| editor-last = Moreau
| editor-first = J. J.
| editor2-last = Panagiotopoulos
| editor2-first = P. D.
| editor3-last = Strang
| editor3-first = G.
| editor3-link = Gilbert Strang
| contribution = Bounded variation in time
| title = Topics in nonsmooth mechanics
| year = 1988
| pages = 1–74
| place = Basel–Boston–Stuttgart
| publisher = Birkhäuser Verlag
| isbn = 3-7643-1907-0
| zbl = 0657.28008}}
*{{Citation
| last1 = Musielak
| first1 = Julian
| last2 = Orlicz
| first2 = Władysław
| author2-link = Władysław Orlicz
| title = On generalized variations (I)
| journal = [[Studia Mathematica]]
| place = Warszawa–Wrocław
| volume = 18
| pages = 13–41
| year = 1959
| url = http://matwbn.icm.edu.pl/ksiazki/sm/sm18/sm1812.pdf
| zbl = 0088.26901
| doi = 10.4064/sm-18-1-11-41
}}. In this paper, Musielak and Orlicz developed the concept of weighted {{math|BV}} functions introduced by [[Laurence Chisholm Young]] to its full generality.
*{{Citation
| first1=Frigyes
| last1=Riesz
| author-link=Frigyes Riesz
| first2=Béla
| last2=Szőkefalvi-Nagy
| author2-link=Béla Szőkefalvi-Nagy
| title=Functional Analysis
| publisher=Dover Publications
| place=New York
| url=https://books.google.com/books?id=jlQnThDV41UC
| year=1990
| isbn=0-486-66289-6
| zbl=0732.47001
}}
*{{Citation
| last = Vol'pert
| first = Aizik Isaakovich
| title = Spaces {{math|BV}} and quasi-linear equations
| journal = [[Matematicheskii Sbornik]]
| series = (N.S.)
| volume = 73 (115)
| language = Russian
| issue = 2
| pages = 255–302
| year = 1967
| url = http://mi.mathnet.ru/eng/msb/v115/i2/p255
| mr = 216338 
| zbl = 0168.07402
}}. A seminal paper where [[Caccioppoli set]]s and {{math|BV}} functions are thoroughly studied and the concept of [[functional superposition]] is introduced and applied to the theory of [[partial differential equation]]s: it was also translated in English as {{Citation
| title = Spaces {{math|BV}} and quasi-linear equations
| journal = [[Mathematics of the USSR-Sbornik]]
| volume = 2
| issue = 2
| pages = 225–267
| year = 1967
| doi = 10.1070/SM1967v002n02ABEH002340
| mr = 216338
| zbl = 0168.07402
| last1 = Vol'Pert
| first1 = A I
| bibcode = 1967SbMat...2..225V
| hdl = 10338.dmlcz/102500
| hdl-access = free
}}.