Giovanni Alberti
Archive
of mathematical papers
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Warning
This page contains all my papers and research notes,
starting from the most recent one.
For every paper, the version stored
here is as close as
possible
to the published one, but may be not exactly the same. In a few
cases I
also kept versions which are different from the published one, for
example because they contain parts that do not appear in the
published
version.
Most papers are also
available in a paper-saving format
(two pages per side, suffix "rdc").
Integration of nonsmooth 2-forms: from Young to Itô and
Stratonovich
with Eugene Stepanov and Dario Trevisan
J. Funct. Anal., 286 (2024), no. 2, art. 110212
[full text.pdf
- full text-rdc.pdf
- MathSciNet
- DOI]
On the geometric structure of
currents tangent to smooth distributions
with Annalisa Massaccesi and Eugene Stepanov
J. Differential Geom., 122 (2022), no. 1, 1-33
[full
text.pdf
- full
text-rdc.pdf - MathSciNet
- DOI]
Lossless analog compression
with Helmut Bölcskei, Camillo De Lellis, Gunther Koliander and Edwin
Riegler
IEEE Trans. Inform. Theory, 65 (2019), no. 11, 7480-7513
[full
text.pdf - MathSciNet
- DOI]
Optimal reinforcing networks for elastic
membranes
with Giuseppe Buttazzo, Serena Guarino Lo Bianco, and Édouard Oudet
Netw. Heterog. Media, 14 (2019), no. 3, 589-615
[full
text.pdf
- full
text-rdc.pdf - MathSciNet
- DOI]
Loss of regularity for the continuity equation with non-Lipschitz
velocity field
with Gianluca Crippa and Anna L. Mazzucato
Ann. PDE, 5 (2019), no. 1, art. 9
[full
text.pdf
- full
text-rdc.pdf - MathSciNet
- DOI]
Exponential self-similar mixing by incompressible flows
with Gianluca Crippa and Anna L. Mazzucato
J. Amer. Math. Soc. (JAMS), 32 (2019), no. 2, 445-490
[full
text.pdf
- full
text-rdc.pdf - MathSciNet
- DOI]
On some geometric properties of
currents and Frobenius theorem
with Annalisa Massaccesi
Rend. Lincei Mat. Appl., 28 (2017), no. 4, 861-869
[full
text.pdf
- full
text-rdc.pdf - MathSciNet
- DOI]
On the structure of continua with
finite length and Gołąb's semicontinuity theorem
with Martino Ottolini
Nonlinear Anal. 153 (2017), 35-55
[postprint.pdf
-
postprint-rdc.pdf
-
revised.pdf
-
revised-rdc.pdf
-
MathSciNet
-
DOI]
Note: compared to the
postprint version (which is essentially the same as the published
one),
in the revised version we have added two pictures, corrected the
proof
of Lemma 2.22 and a few small mistakes, and modified the
definition of
delta-partition in Subsection 2.7, in order to make the statement
of
Proposition 2.8 stronger.
Eulerian, Lagrangian and
Broad continuous solutions to a balance law with non-convex flux.
I
with Stefano Bianchini and Laura Caravenna
J. Differential Equations, 261 (2016), no. 8, 4298-4337
[full
text.pdf
- full
text-rdc.pdf - MathSciNet
-
DOI]
Lossless linear analog
compression
with Helmut Bölcskei, Camillo De Lellis,
Günther Koliander, Erwin Riegler
in "Proceedings of the IEEE International Symposium on Information
Theory", volume 2016, pp. 2789-2793
Institute of Electrical and Electronics Engineers, New York, 2016
[full
text.pdf
- DOI]
On the differentiability
of Lipschitz functions with respect to measures in the Euclidean
space
with Andrea Marchese
Geom. Funct. Anal. (GAFA), 26 (2016), no. 1, 1-66
[full
text.pdf
- full
text-rdc.pdf - MathSciNet
- DOI]
Reduction on
characteristics for continuous solutions of a scalar balance
law
with Stefano Bianchini and Laura Caravenna
in "Hyperbolic problems: theory, numerics, applications"
(Proceedings
of the 14th International Conference on Hyperbolic
Problems (HYP2012), Padua, June 25-29, 2012), part III (contributed
talks), pp. 399-406.
Edited by F. Ancona, A. Bressan, P.
Marcati,
A. Marson.
AIMS Series on Applied Math., volume 8.
American Institute of Mathematical Science, Springfield, 2014
[full
text.pdf
- full
text-rdc.pdf - complete
volume -
ISBN: 978-1-60133-017-8]
Exponential self-similar
mixing and loss of regularity for continuity equations
with Gianluca Crippa and Anna L. Mazzucato
C. R. Acad. Sci. Paris, Ser. I, 352 (2014), no. 11, 901-906
[full
text.pdf
- full
text-rdc.pdf - MathSciNet
-
DOI]
On the Lp-differentiability
of
certain classes of functions
with Stefano Bianchini and Gianluca Crippa
Rev. Mat. Iberoam., 30 (2014), no. 1, 349-367
[full
text.pdf
- full
text-rdc.pdf - MathSciNet
-
DOI]
A uniqueness result for
the continuity equation in two dimensions
with Stefano Bianchini and Gianluca Crippa
J. Eur. Math. Soc. (JEMS), 16 (2014), no. 2, 201-234
[full
text.pdf
- full
text-rdc.pdf - MathSciNet
-
DOI]
Structure of level sets
and Sard-type properties of Lipschitz maps
with Stefano Bianchini and Gianluca Crippa
Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5), 12 (2013), no. 4, 863-902
[full
text.pdf
- full
text-rdc.pdf - MathSciNet
-
DOI]
Generalized N-property
and Sard theorem for Sobolev maps
Rend. Lincei Mat. Appl., 23 (2012), no. 1, 477-491
[full
text.pdf
- full
text-rdc.pdf - MathSciNet
- DOI]
Quasistatic evolution of
sessile drops and contact angle hysteresis
with Antonio DeSimone
Arch. Rational Mech. Anal., 202 (2011), no. 1, 295-348
[full
text.pdf
- full
text-rdc.pdf - MathSciNet
-
DOI]
Differentiability of
Lipschitz functions, structure of null sets, and other problems
with Marianna Csörnyei and David Preiss (lecture delivered by
M. Csörnyei)
in "Proceedings of the international congress of mathematicians (ICM
2010, Hyderabad, India, August 19-27, 2010)", volume 3 (invited
lectures), pp. 1379-1394.
Edited by R. Bhatia et al.
Hindustan Book
Agency, New Delhi, 2010
[full
text.pdf
- full
text-rdc.pdf - MathSciNet
- DOI
- ISBN: 978-981-4324-30-4]
Two-dimensional
transport equation with Hamiltonian vector fields
with Stefano Bianchini and Gianluca Crippa
in "Hyperbolic problems: theory, numerics and applications"
(proceedings of the 12th International Conference on Hyperbolic
Problems (HYP2008), University of Maryland, June 9-13, 2008), part 2
(contributed talks), pp.
337-346.
Edited by E. Tadmor, J.-G. Liu, A. Tzavaras.
Proceedings of
Symposia in Applied Mathematics, 67.
American Mathematical
Society, Providence 2009
[full
text.pdf
- full
text-rdc.pdf - MathSciNet
- DOI
- ISBN: 978-0-8218-4730-5]
Uniform energy
distribution for an isoperimetric problem with long-range
interactions
with Rustum Choksi and Felix Otto
J. Amer. Math. Soc., 22 (2009), no. 2, 569-605
[full
text.pdf
- full
text-rdc.pdf - MathSciNet
-
DOI]
Calcolo delle variazioni [Calculus of Variations]
in: "Enciclopedia italiana di scienze, lettere ed arti. XXI
Secolo. Settima Appendice", volume 1, pp. 252-255.
Edited by T.
Gregory et al.
Istituto della Enciclopedia Italiana fondata da Giovanni
Treccani, Roma 2006
[full
text.pdf]
On maps whose
distributional Jacobian is a measure
Real analysis exchange. Report on the "Summer Symposium in Real
Analysis XXXI" (Trinity College, Oxford, England, August 13-15,
2007),
pp. 153-162.
Michigan State University Press, 2008
[full
text.pdf
- full
text-rdc.pdf - MathSciNet]
Geometric measure theory
in the "Encyclopedia of mathematical physics",
volume 2, pp. 520-527.
Edited by J.-P. Françoise, G.L.
Naber, S.T. Tsou.
Academic Press / Elsevier Science, Oxford
2006
[full
text.pdf
- full
text-rdc.pdf
- MathSciNet
- DOI
- ISBN: 978-0-12-512666-3]
Distributional Jacobian
and singularities of Sobolev
maps
Ricerche Mat., 54 (2005), no. 2, 375-394
[full
text.pdf
- full
text-rdc.pdf
- MathSciNet]
Variational
convergence for functionals of Ginzburg-Landau type
with Sisto Baldo and Giandomenico Orlandi
Indiana Univ. Math. J. 54 (2005), no. 5, 1411-1472
[full
text.pdf
- full
text-rdc.pdf - MathSciNet
-
DOI]
Structure of null sets
in the plane and applications
with Marianna Csörnyei and David Preiss (lecture delivered by
G. Alberti)
in "European Congress of Mathematics. Proceedings of the 4th
Congress
(4ECM) held in Stockholm,
June 27-July 2, 2004", pp. 3-22.
Edited by A.
Laptev.
European Mathematical Society (EMS),
Zürich
2005
[full
text.pdf
- full
text-rdc.pdf - MathSciNet
- DOI
- ISBN 978-3-03719-009-8]
BV has the bounded
approximation property
with Marianna Csörnyei, Aleksander Pełczyński and David Preiss
J. Geom. Anal. 15 (2005), no. 1, 1-7
[full
text.pdf
- full
text-rdc.pdf - MathSciNet
-
DOI]
Wetting
of rough surfaces: a
homogenization
approach
with Antonio DeSimone
Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 461 (2005), no.
2053,
79-97
[full
text.pdf
- full
text-rdc.pdf - MathSciNet
-
DOI]
Aritmetica finita e
crittografia a chiave pubblica. Un
percorso
didattico per studenti delle scuole medie superiori [Arithmetic
and
public-key cryptography. An educational journey for high-school
students]
in "Ricordando Franco Conti", pp. 1-29.
Edited by
A. Abbondandolo, M. Giaquinta, F. Ricci.
Pubblicazioni del Centro di
Ricerca Matematica E. De Giorgi, Scuola Normale Superiore,
Pisa 2004
[full
text.pdf
- full
text-rdc.pdf
- MathSciNet
- ISBN: 978-8876421372]
Note: a preliminary version
of
these notes appeared in 2001 under the title of "Aritmetica e
crittografia [Arithmetic and cryptography]"
Functions
with prescribed
singularities
with Sisto Baldo and Giandomenico Orlandi
J. Eur. Math. Soc. (JEMS) 5 (2003), no. 3, 275-311
[full
text.pdf
- full
text-rdc.pdf
- MathSciNet
-
DOI]
The
calibration method for the Mumford-Shah functional and free
discontinuity
problems
with Guy Bouchitté and Gianni Dal Maso
Calc. Var. Partial Differential
Equations,
16 (2003), no. 3, 299-333
[postprint.pdf
-
postprint-rdc.pdf
-
extended.pdf
-
extended-rdc.pdf
-
MathSciNet
-
DOI]
Note: the extended version
contains some remarks and paragraphs (not
numbered) not included in the postprint version (which is
essentially
the same as the published one)
Un risultato di
convergenza
variazionale per funzionali di tipo
Ginzburg-Landau
in dimensione qualunque
[A variational convergence result for functionals of
Ginzburg-Landau
type in any dimension]
Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8), 4
(2001), no.
2,
289-310
[ full
text.pdf
- full
text-rdc.pdf - MathSciNet
- EuDML]
[English translation
(unpublished): full
text.pdf
- full
text-rdc.pdf]
Denjoy-Young-Saks
theorem for
approximate derivatives revisited
with Marianna Csörnyei, Miklós Laczkovich and David
Preiss
Real Anal. Exchange,
26
(2000/01), no. 1, 485-488
[full
text.pdf
- full
text-rdc.pdf
- MathSciNet
- Project
Euclid]
On a long standing
conjecture of E.
De Giorgi: symmetry in 3D for
general
nonlinearities and a local minimality property
with Luigi Ambrosio and Xavier Cabré
Acta Appl. Math., 65 (2001), no. 1-3, 9-33
[full
text.pdf
- full
text-rdc.pdf
- MathSciNet
-
DOI]
A new
approach to variational problems with multiple scales
with Stefan Müller
Comm. Pure Appl. Math., 54 (2001), no. 7, 761-825
[full
text.pdf
- full
text-rdc.pdf - MathSciNet
-
DOI]
Some remarks about a
notion of
rearrangement
Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 29 (2000), no. 2,
457-472
[full
text.pdf
- full
text-rdc.pdf
- MathSciNet
- Numdam
- EuDML]
Variational
models for phase transitions, an approach via
Gamma-convergence
in L. Ambrosio, N. Dancer: "Calculus of variations and partial
differential equations. Topics on geometrical evolution problems and
degree theory. Papers from the Summer School held in Pisa, September
1996", pp.
95-114.
Edited by G. Buttazzo, A. Marino, M.K.V. Murthy.
Springer-Verlag,
Berlin, 2000
[full
text.pdf
- full
text-rdc.pdf
- MathSciNet
- DOI
- ISBN 978-3-540-64803-1]
The calibration method
for the
Mumford-Shah functional
with Guy Bouchitté and Gianni Dal Maso
C. R. Acad. Sci. Paris,
Sér.
I Math., 329 (1999), no. 3, 249-254
[full
text.pdf
- MathSciNet
-
DOI]
A geometrical approach
to monotone
functions in Rn
with Luigi Ambrosio
Math. Z., 230 (1999), no. 2, 259-316
[full
text.pdf
- full
text-rdc.pdf -
MathSciNet
-
DOI]
Phase transition with
line-tension effect
with Guy Bouchitté and Pierre Seppecher
Arch. Rational Mech. Anal., 144
(1998), no. 1, 1-46
[full
text.pdf
- full
text-rdc.pdf - MathSciNet
-
DOI]
A
nonlocal anisotropic model for phase transitions: asymptotic
behaviour
of rescaled energies
with Giovanni Bellettini
European J. Appl. Math., 9 (1998), no. 3, 261-284
[postprint.pdf
- postprint-rdc.pdf
-
extended.pdf
-
extended-rdc.pdf
- MathSciNet
-
DOI]
Note: compared to the
postprint version (which is essentially the same as the published
one)
the
extended version
contains an additional chapter where we prove the convergence of
certain nonlocal interaction energies to standard convex
functionals of
the gradients
A nonlocal anisotropic
model for
phase transitions. I. The optimal
profile
problem
with Giovanni Bellettini
Math. Ann., 310 (1998), no. 3, 527-560
[full
text.pdf
- full
text-rdc.pdf - MathSciNet
-
DOI]
A note about the theory
of SBV
functions
with Carlo Mantegazza
Boll. Un. Mat. It. B (7), 11 (1997), no. 2, 375-382
[full
text.pdf
- full
text-rdc.pdf - MathSciNet]
Surface tension in Ising
systems with
Kac potential
with Giovanni Bellettini, Marzio Cassandro and Errico Presutti
J. Statist. Phys., 82
(1996), no. 3-4,
743-796
[full
text.pdf
- full
text-rdc.pdf - MathSciNet
-
DOI]
Boundary effects in
phase transitions
with Guy Bouchitté and Pierre Seppecher
in "Curvature flows and related topics. Proceedings of the Second
International Conference held in Levico, June 27-July 2,
1994", pp. 1-11.
Edited by A. Damlamian, J. Spruck, A.
Visintin.
Gakuto International Series, Mathematical Sciences and Applications,
5.
Gakkotosho,
Tokyo,
1995
[full
text.pdf
- full
text-rdc.pdf - MathSciNet
- ISBN: 978-4762504143]
Un résultat
de perturbations
singuliéres avec la norme H1/2
with Guy Bouchitté and Pierre Seppecher
C.R. Acad. Sci. Paris,
Sér.
I Math., 319 (1994), no. 4, 333-338
[full
text.pdf
- MathSciNet
- Gallica]
Non-occurrence of gap
for
one-dimensional autonomous functionals
with Francesco Serra Cassano
in "Calculus of variations, homogenization and continuum mechanics.
Proceedings of the workshop held in Marseille, June 21-25, 1993",
pp.
1-17.
Edited by G. Bouchitté, G. Buttazzo, P. Suquet.
Series on
Advances in Mathematics for Applied Sciences, 18.
World Scientific
Publishing Co., River Edge, NJ, 1994
[full
text.pdf
- full
text-rdc.pdf - MathSciNet
- ISBN: 978-9810217839]
Gap phenomenon for
autonomous
functionals
with Pietro Majer
J. Convex Anal., 1 (1994), no. 1, 31-45
[full
text.pdf
- full
text-rdc.pdf - MathSciNet
-
EuDML]
On the structure of
singular sets of
convex functions
Calc. Var. Partial Differential Equations, 2 (1994), no. 1, 17-27
[full
text.pdf
- full
text-rdc.pdf - MathSciNet
-
DOI]
Singular perturbation
problems with a
compact support semilinear term
with Luigi Ambrosio and Giuseppe Buttazzo
Asymptotic Anal., 8 (1994), no. 3, 247-258
[full
text.pdf
- full
text-rdc.pdf - MathSciNet
-
DOI]
Local mappings on spaces
of
differentiable functions
with Giuseppe Buttazzo
Manuscripta Math., 79 (1993), no. 1, 81-97. Errata, ibid.,
81
(1993), no. 3-4, 445-446
[corrected
version.pdf
- corrected
version-rdc.pdf - MathSciNet
-
DOI]
Note: the version
stored here includes all corrections from the
erratum
Rank one property for
derivatives of
functions with bounded variation
Proc. Roy. Soc. Edinburgh Sect. A, 123 (1993), no. 2, 239-274
[full
text.pdf
- full
text-rdc.pdf -
MathSciNet
-
DOI]
Integral representation
of local
functionals
Ann. Mat. Pura Appl. (4), 165 (1993), no. 1, 49-86
[full
text.pdf
- full
text-rdc.pdf - MathSciNet
-
DOI]
On the singularities of
convex
functions
with Luigi Ambrosio and Piermarco Cannarsa
Manuscripta Math., 76 (1992), no. 3-4, 421-435
[full
text.pdf
- full
text-rdc.pdf -
MathSciNet
-
DOI]
Integral representation
of
functionals defined on Sobolev spaces
with Giuseppe Buttazzo
in "Composite media and homogenization theory. Proceedings of the
workshop held in Trieste, January 15-26, 1990", pp.
1-12.
Edited by G. Dal Maso, G. Dell'Antonio.
Progress in Nonlinear
Differential Equations and their Applications, 5.
Birkhäuser
Boston, Boston 1991
[full
text.pdf
- full
text-rdc.pdf - MathSciNet
- ISBN: 978-1-4684-6787-1]
A
Lusin type theorem for gradients
J. Funct. Anal., 100 (1991), no. 1, 110-119
[full
text.pdf
- full
text-rdc.pdf - MathSciNet
-
DOI]