RICERCA ITALIANA     

Programmi di ricerca simili:

• 1 - Metodi variazionali nella teoria del trasporto ottimo di massa e nella teoria geometrica della misura
• 2 - Problemi variazionali con scale multiple
• 3 - Analisi matematica nei problemi inversi
• 4 - Metodi Variazionali ed Equazioni Differenziali Nonlineari
• 5 - Metodi variazionali e topologici nello studio di fenomeni non lineari
• 6 - Modellizzazione Matematica ed Analisi dei Problemi a Frontiera Libera
• 7 - Metodi variazionali ed equazioni differenziali nonlineari
• 8 - Metodi numerici avanzati per equazioni alle derivate parziali di interesse applicativo
• 9 - Problemi a frontiera libera, transizioni di fase e modelli di isteresi
• 10 - Teoria Matematica del Controllo: Controllabilita`, Ottimizzazione, Stabilita`

Classificazione scientifico-disciplinare

• Area scientifico disciplinare: Scienze matematiche e informatiche
  • ANALISI MATEMATICA

Classificazione brevettuale

• PHYSICS
  • COMPUTING; CALCULATING; COUNTING (score computers for games A63; combinations of writing applicances with computing devices B43K29/08)
    • IMAGE DATA PROCESSING OR GENERATION, IN GENERAL (specially adapted for particular applications, see the relevant subclasses, e.g. G06K, G09G, H04N) [N9408]
  • MEASURING (counting G06M); TESTING
    • MEASURING LINEAR OR ANGULAR SPEED, ACCELERATION, DECELERATION, OR SHOCK; INDICATING PRESENCE, ABSENCE, OR DIRECTION, OF MOVEMENT (measuring or rec ording blood flow A61B5/02, A61B8/06; monitoring speed or deceleration of electrically-propelled vehicles B60L3/00; vehicle lighting systems adapted to indicate speed B60Q1/54; determining position or course in navigation, measuring ground distance in geodesy or surveying G01C; combined measuring devices for measuring two or more variables of movement G01C23/00; measuring velocity of sound G01H; measuring velocity of light G01J7/00; measuring direction or velocity of solid objects by reception or emission of radiowaves or other waves and based on propagation effects, e.g. Doppler effect, propagation time, direction of propagation, G01S; measuring speed of nuclear radiation G01T; measuring acceleration of gravity G01V; [N: measuring, recording the speed of trains B61L23/00; speed indicators incorporated in motor vehicles B60K35/00; measuring frequency or phase G01R; traffic control G08G])

Classificazione geografica

• Regione: Toscana

Bibliografia

Due to the limited space available this list is not exhaustive.

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[4] L. AMBROSIO, A. PRATELLI: Existence and stability results in the L^1
theory of optimal transportation. Lecture Notes in Mathematics, Vol. 1813, 2003.
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128 (1977).
[6] F. OTTO: The geometry of dissipative evolution equations: the porous
medium equation. Comm. PDE, 26 (2001).
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[8] L. AMBROSIO: Transport equation and Cauchy problem for BV vector
fields. Inventiones Mathematicae, in press.
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Well--posedness for a class of hyperbolic systems of
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perimeter in the Heisenberg group. Math. Ann., 321 (2001).
[13] B. FRANCHI, R. SERAPIONI, F. SERRA CASSANO: On the structure of
finite perimeter sets in step 2 Carnot groups. J. Geom. Anal., 13 (2003).
[14] L. AMBROSIO: Some fine properties of sets of finite perimeter in
Ahlfors regular metric measure spaces. Adv. Math., 159 (2001).
[15] T. ILMANEN: Convergence of the Allen-Cahn equation to Brakke's
motion by mean curvature. J. Differential Geom., 38 (1993).
[16] E. ACERBI, I. FONSECA, G. MINGIONE: A model for mixtures of
micromagnetic materials allowing existence and regularity, Progr.
Nonlinear Differential Equations Appl. 35 (2002)
[17] E. ACERBI, G. MINGIONE: Regularity results for a class of
quasiconvex functionals with nonstandard growth, Ann. Scuola Norm. Sup.
Pisa Cl. Sci. (4) 30 (2001)
[18] E. ACERBI, G. MINGIONE: Regularity results for stationary
electrorheological fluids, Arch. Rational Mech. Anal. 164 (2002)
[19] J. BALL: Convexity conditions and existence theorems in nonlinear
elasticity, Arch. Rational Mech. Anal. 63 (1977)
[20] A. DESIMONE, R.V. KOHN, S. MULLER, F. OTTO: Magnetic
microstructures - a paradigm of multiscale problems, ICIAM 99
(Edinburgh), Oxford University Press, Oxford, 2000
[21] F. DUZAAR, G. MINGIONE: Regularity of degenerate elliptic
problems via p-harmonic approximation, Ann. Inst. H. Poincaré 21 (2004)
[22] M. GIAQUINTA, D. MUCCI: Weak and strong density results for the
Dirichlet energy, J. Eur. Math. Soc. 6 (2004)
[23] P. MARCELLINI: Regularity of minimizers of integrals of the Calculus
of Variations with non standard growth conditions, Arch. Rational Mech.
Anal. 105 (1989)
[24] G. ALBERTI, G. BOUCHITTE', G. DAL MASO: The calibration method for
the Mumford-Shah functional and free discontinuity problems, Calc. Var.
Partial Differential Equations, 16 (3) (2003), 299-333.
[25] G. ALBERTI, S. BALDO, G. ORLANDI: Functions with prescribed
singularities, J. Eur. Math. Soc. (JEMS), 5 (3) (2003), 275-311.
[26] L. AMBROSIO, N. FUSCO, D. PALLARA: Functions of bounded variation
and free discontinuity problems, Oxford Mathematical Monographs,
Clarendon Press, Oxford (2000).
[27] G. BOUCHITTE, G. BUTTAZZO, L. DE PASCALE: A p-Laplacian
approximation for some mass optimization problems, J. Optim. Theory
Appl., 118 (1) (2003), 1-25.
[28] B. DACOROGNA, P. MARCELLINI: Implicit partial differential
equations. Progress in Nonlinear Differential Equations and their
Applications 37, Birkhäuser Verlag, Basel (1999), xii+273 pp.
[29] G. DAL MASO: An introduction to Gamma-convergence, Progress in
Nonlinear Differential Equations and their Applications 8, Birkhäuser
Verlag, Basel (1993), xiv+340 pp.
[30] M. GIAQUINTA, G. MODICA, J. SOUCEK: Cartesian currents in the
calculus of variations I, II. Ergebnisse der Mathematik und ihrer
Grenzgebiete vol. 37-38, Springer Verlag, Berlin (1998).
[31] E. ACERBI, G. DAL MASO: New lower semicontinuity results for polyconvex
integrals. Calc. Var. Partial Differential Equations 2 (1994), 329-372.
[32] A. BRAIDES, G. DAL MASO: Non-local approximation of the Mumford-Shah
functional. Calc. Var. Partial Differential Equations 5 (1997), 293-322.
[33] A. BRAIDES, G. DAL MASO, A. GARRONI: Variational formulation of
softening phenomena in fracture mechanics: the one-dimensional case.
Arch. Rational Mech. Anal. 146 (1999), 23-58.
[34] G. DAL MASO, I. FONSECA, G. LEONI, M. MORINI: Higher order
quasiconvexity reduces to quasiconvexity. Arch. Rational Mech. Anal. 171
(2004), 55-81.
[35] G. FRIESECKE, R.D. JAMES, M.G. MORA, S. MULLER: Derivation of nonlinear
bending theory for shells from three dimensional nonlinear elasticity by
Gamma-convergence. C.R. Acad. Sci. Paris Sér. I 336 (2003), 697-702.
[36] G. LEONI, M. MORINI: Some remarks on the analyticity of minimizers of
free discontinuity problems. J. Math. Pures Appl. 9 (2003), 533-551.
[37] G. BELLETTINI, V. CASELLES, M. NOVAGA: The total variation flow in
R^n. J. Diff.Eq. 184 (2002) 475-525.
[38] G. BELLETTINI, M. NOVAGA, M. PAOLINI: On a crystalline variational
problem, part I: first variation and global L^infty-regularity. Arch.
Rational Mech. Anal. 157 (2001) 165-191.
[39] G. BELLETTINI, M. NOVAGA, M. PAOLINI: On a crystalline variational
problem, part II: BV-regularity and structure of minimizers on facets.
Arch. Rational Mech. Anal. 157 (2001) 193-217.
[40] A. BRAIDES: Gamma-convergence for Beginners. Oxford University Press.
Oxford. 2002
[41] F. BETHUEL, H. BREZIS, F. HELEIN: Ginzburg-Landau vortices.
Birkhäuser Boston 1994
[42] J.M. MOREL, S. SOLIMINI: Variational Methods in Image Segmentation,
Birkhauser, Basel, 1994
[43] G. ALBERTI, S. BALDO, G.ORLANDI: Functions with prescribed
singularities" J. Eur. Math. Soc. (JEMS) 5, 3 (2003), 275-311.
[44] A. BRAIDES, A. DEFRANCESCHI: Homogenezation of multiple integrals.
Oxford Lecture notes in Mathematics, Oxford University Press (1998).
[45] M. CARRIERO, A. LEACI, F. TOMARELLI: Calculus of Variations and Image
Segmentation, J.of Physiology Paris, 97, (2003) 343-353.
[46] G.DAL MASO, M. NEGRI, D. PERCIVALE: Linearized elasticity as Gamma
limit of finite elasticity, Set-Valued Anal 10, (2002) 165-183.
[47] G. CRASTA, I.FRAGALA', F. GAZZOLA: A sharp upper bound for the
torsional rigidity of rods by means of web functions,
Arch.Rat.Mech.Anal. 164 (2002) 189-211.
[48] A.BONNET, G. DAVID: Crack-tip is a global Mumford-Shah minimizer,
Asterisque, 274(2001)
[49] A. BLAKE, A. ZISSERMAN: Visual Reconstruction,MIT Press, Cambridge 1987
[50] G. DAL MASO, R. TOADER: A model for the quasi-static growth of
brittle fractures: existence and approximation results, to appear
in Arch.Rat.Mech.Anal.
[51] D. MUMFORD, J. SHAH: Optimal approx. by piecewise smooth functions
and associated variational pbs., Comm.PureAppl.Math., XLII 1989, 577-685.
[52] C. VILLANI: Topics in Optimal Transportation, Graduate Series in
Mathematics, 54, AMS, 2003
[53] H. BREZIS, E.H. LIEB: Sobolev inequalities with a remainder term,
J. Funct. Anal., 62 (1985), 73-86
[54] M. CARRIERO, A. LEACI, F. TOMARELLI: Strong solution for an Elastic
Plastic Plate, Calc. Var., 2 (1994), 219--240.
[55] A. CIANCHI, N. FUSCO: Functions of bounded variation and rearrangements,
Arch. for Rat. Mech. and Anal. 165 (2002), 1-40
[56] I. FONSECA, N. FUSCO, P. MARCELLINI: On the total variation of the
jacobian, J. of Funct. Anal. 207 (2004), 1-32.
[57] J.D. BENAMOU, Y. BRENIER: A computational fluid mechanics
approach to the Monge-Kantorovich mass transfer problem.
Numerische Math. 84 (2000), 375-393.

Parole Chiave

PROBLEMI CON DISCONTINUITA' LIBERE; TEORIA GEOMETRICA DELLA MISURA; GAMMA-CONVERGENZA E RILASSAMENTO; REGOLARITA' DELLE SOLUZIONI; PROBLEMI DI TRASPORTO OTTIMALE