BOOKS and LECTURE NOTES
To appear in the Monographs of the European Mathematical Society.
In Press. Volume 219 of the Annals of Mathematics Studies, Princeton University Press
In Harmonic Analysis and Applications. C. Kenig, F. Lin, S. Mayboroda, T. Toro editors. Vol 27 of IAS/Park City Mathematics Series. 2020 AMS
Chapter in the book The Abel Prize 2013-2017. H. Holden and R. Piene (editors). Springer.
The paper, in italian, has appeared first in the journal "il Volterriano". The file which can be downloaded here contains minor modifications and has been published by Rivista dell'UMI.
Proceedings of CMSA Harvard
Nonlinear analysis in geometry and applied mathematics. Part 2, 23–49,
Harv. Univ. Cent. Math. Sci. Appl. Ser. Math., 2, Int. Press, Somerville, MA, 2018.
The paper, in italian, has appeared first in the journal "il Volterriano". The file which can be downloaded here contains minor modifications and has been published by Rivista dell'UMI.
Zurich Lectures in Advanced Mathematics. European Mathematical Society (EMS), Zürich.
PROCEEDINGS, SURVEYS and EXPOSITORY ARTICLES in GMT
Preprint. To appear in the Proceedings of the 2022 ICM.
2017 Matrix Annals 193-205 Springer International Publishing, 2018.
Boll. Unione Mat. Ital. 9 (2016), no. 1, 3–67.
Surveys in differential geometry 2016. Advances in geometry and mathematical physics, 1–83, Surv. Differ. Geom., 21, Int. Press, Somerville, MA, 2016.
Current developments in mathematics 2014, 153–229, Int. Press, Somerville, MA, 2016.
Proceedings of the International Congress of Mathematicians Hyderabad, India, 2010
Transport equations and multi-D hyperbolic conservation laws, 61–74, Lect. Notes Unione Mat. Ital., 5, Springer, Berlin, 2008.
Surveys in differential geometry, Vol. VIII (Boston, MA, 2002), 75–107, Int. Press, Somerville, MA, 2003.
EXPOSITORY ARTICLES and SURVEYS on the H-PRINCIPLE
Philos. Trans. Roy Soc. A, 380 (2022), no. 2218, 16pp.
Surveys in differential geometry 2017.
Bull. Amer. Math. Soc. (N.S.) 54 (2017), no. 2, 247–282.
Forthcoming in Memorial Volume for Professor John Nash, eds. Joseph Kohn and Hong Jun, World Scientific Publishers, 2017
Eur. Math. Soc. Newsl. No. 95 (2015), 19–24.
European Congress of Mathematics, 13–29, Eur. Math. Soc., Zürich, 2013.
Bull. Amer. Math. Soc. 49, 347-375, 2012
Boll. Unione Mat. Ital. (9) 1 (2008), no. 3, 873–879
EXPOSITORY ARTICLES in HYPERBOLIC SYSTEMS and TRANSPORT EQUATIONS
Hyperbolic problems: theory, numerics and applications, 269–278, Proc. Sympos. Appl. Math., 67, Part 1, Amer. Math. Soc., Providence, RI, 2009.
Journées équations aux dérivées partielles (2010), Exp. No. 6, 10 p.
Hyperbolic problems: theory, numerics and applications. I, 105–112, Yokohama Publ., Yokohama, 2006
Discrete Contin. Dyn. Syst. Ser. S 1 (2008), no. 3, 405–426.
Handbook of differential equations: evolutionary equations. Vol. III, 277–382, Handb. Differ. Equ., Elsevier/North-Holland, Amsterdam, 2007.
Séminaire Bourbaki. Vol. 2006/2007. Astérisque No. 317 (2008), Exp. No. 972, viii, 175–203.
INTERIOR REGULARITY for AREA MINIMIZING CURRENTS
Preprint
Preprint
Preprint
Geom. Funct. Anal., 30(5):1224-1336, 2020.
J. Differential Geom. 116 (2020), no. 1, 125-185
Ann. PDE 3 (2017), no. 2, Art. 18, 85 pp.
Trans. Amer. Math. Soc. 370 (2018), no. 3, 1783–1801
Comm. Pure Appl. Math. 70, 1402-1421
J. Reine Angew. Math. 734, 99-144
Ann. of Math. (2) 183 (2016), no. 2, 577–617.
Ann. of Math. (2) 183 (2016), no. 2, 499–575.
Geom. Funct. Anal. 24 (2014), no. 6, 1831–1884.
To appear in the Proceedings for the 2009 Conference in honor of De Giorgi and Stampacchia, held in Erice Discrete and Continuous Dynamical Systems Volume 31, Issue 4, Pages : 1249 - 1272, 2011
BOUNDARY REGULARITY for AREA MINIMIZING CURRENTS
Preprint
Nonlinear Anal. 230 (2023), no. 113235, 10 pp. Volume in honor of Emmanuele DiBenedetto
J. Differential Geom. 122 (2022), no. 2, 205-222
To appear in Memoirs of the American Mathematical Society
MULTIPLE VALUED FUNCTIONS
Indiana Univ. Math. J. 72 (2023), no. 4, 1367-1428
Comm. Pure Appl. Math. 75 (2022), no. 1, 83-127
Comment. Math. Helv. 93 (2018) no. 4, 737-779
Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 14 (2015), no. 4, 1239–1269.
Annales Academiae Scientiarum Fennicae vol. 36 pp. 393-410 (2011)
Memoirs of the AMS 211 (2011), no. 991.
Ann. Mat. Pura Appl. (4) 183 (2004), no. 1, 79–95.
OTHER WORKS in GEOMETRIC MEASURE THEORY
J. Math. Pures Appl. (9) 155 (2021), 83-110
Ann. Fac. Sci. Toulouse Math. (6) 30 (2021), no. 4, 899-960
Ann. Inst. Fourier (Grenoble) 68 (2018) no 5, 1909-1986
Adv. Calc. Var. 12 (2019) no. 2, 211-223
J. Eur. Math. Soc. (JEMS) 19 (2017), no. 8, 2219–2240
Adv. Calc. Var. 7, pp. 539-545, 2014
Manuscripta Math. 142 (2013), 215-232.
J. Math. Pures Appl. (9) 100 (2013), 391-409.
J. Differential Geom. 95 (2013), no. 3, 355–388.
J. Reine Angew. Math. 644 (2010), 47–99.
Proc. Roy. Soc. Edinburgh Sect. A 132 (2002), no. 4, 815–842.
OTHER WORKS in MINIMAL SURFACES and GEODESICS
J. Differential Geom. 112(3):411-445, 2019.
Comm. Pure Appl. Math. 61 (2008), no. 11, 1540–1602.
Topology 44 (2005), no. 1, 25–45.
INCOMPRESSIBLE EULER EQUATIONS
Appendix G in Alexander Migdal, Statistical equilibrium of circulating fluids, Physics Reports, 1011 (2023)
Anal. PDE 15 (2022), no. 8, 2003-2059
Comm. Pure Appl. Math. 72 (2019), no. 2, 229-274
Comm. Pure Appl. Math. 69 (2016), no. 9, 1613–1670.
Ann. of Math. (2) 182 (2015), no. 1, 127–172.
J. Eur. Math. Soc. (JEMS) 16 (2014), no. 7, 1467–1505.
Inventiones Mathematicae 193, Issue 2 (2013), Page 377-407
Comm. Math. Phys. 305 (2011), 351-361
Arch. Ration. Mech. Anal. 195 (2010), no. 1, 225–260.
Ann. of Math. (2) 170 (2009), no. 3, 1417–1436.
INCOMPRESSIBLE NAVIER STOKES
To appear in Comm. Pure Appl. Anal. in a volume in honor of Vladimir Sverak. Published online.
Comm. Math. Phys. 400 (2023), no. 3, 1507-1533
Comm. Pure Appl. Math. 73 (2020), no. 3, 609–663.
Comm. Math. Phys. 362 (2018) no. 2, 659-688
RIGIDITY ESTIMATES
Calc. Var. 43 (2012) 347-354
Calc. Var. Partial Differential Equations 26 (2006), no. 3, 283–296.
J. Differential Geom. 69 (2005), no. 1, 75–110.
ISOMETRIC EMBEDDINGS
Rev. Mat. Iberoam. 34 (2018) no. 3, 1119-1152
Nonlinear Partial Differential Equations Abel Symposia Volume 7, 2012, pp 83-116
TRANSPORT EQUATIONS
Smoothing does not give a selection principle for transport equations with bounded autonomous fields
Ann. Math. Que'. 46 (2022), no. 1, 27-39 A volume in honor of Alexander Shnirelman
Arch. Ration. Mech. Anal. 240(2):1055-1090, 2021.
Calc. Var. Partial Differential Equations 55 (2016), no. 5, Paper No. 128, 17 pp.
J. Reine Angew. Math. 616 (2008), 15–46.
Indiana Univ. Math. J. 55 (2006), no. 1, 1–13.
Perspectives in nonlinear partial differential equations, 31–67, Contemp. Math., 446, Amer. Math. Soc., Providence, RI, 2007.
HYPERBOLIC SYSTEMS OF CONSERVATION LAWS
To appear in Arch. Ration. Anal. Mech.
Hyperbolic problems: theory, numerics, applications, 1–10, AIMS Ser. Appl. Math., 8, Am. Inst. Math. Sci. (AIMS), Springfield, MO, 2014.
Comm. Pure Appl. Math. 68 (2015), no. 7, 1157–1190.
Duke Math. J. 127 (2005), no. 2, 313–339.
Comm. Partial Differential Equations 29 (2004), no. 9-10, 1635–1651.
Int. Math. Res. Not. 2003, no. 41, 2205–2220.
SCALAR CONSERVATION LAWS AND HAMILTON JACOBI EQUATIONS
Comm. Partial Differential Equations 40 (2015), no. 8, 1543–1557.
Arch. Ration. Mech. Anal. 200 (2011) 1051-1073
Arch. Ration. Mech. Anal. 200 (2011) 1003-1021
J. Hyperbolic Differ. Equ. 1 (2004), no. 4, 813–826.
Comm. Pure Appl. Math. 58 (2005), no. 7, 989–998.
J. Math. Pures Appl. (9) 82 (2003), no. 10, 1343–1367.
Quart. Appl. Math. 62 (2004), no. 4, 687–700.
Ann. Inst. H. Poincaré Anal. Non Linéaire 20 (2003), no. 6, 1075–1085.
Arch. Ration. Mech. Anal. 170 (2003), no. 2, 137–184
VECTORIAL CALCULUS OF VARIATIONS
C. R. Math. Acad. Sci. Paris 348 (2010), no. 17-18, 973–976
C. R. Math. Acad. Sci. Paris 343 (2006), no. 5, 367–370
C. R. Math. Acad. Sci. Paris 337 (2003), no. 4, 233–238.
Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 2 (2003), no. 3, 521–549.
Nonlinear Anal. 53 (2003), no. 7-8, 1101–1114.
J. Elasticity 65 (2001), no. 1-3, 1–31 (2002).
PHASE TRANSITIONS
Math. Ann. 338 (2007), no. 1, 119–146.
J. Eur. Math. Soc. (JEMS) 5 (2003), no. 2, 107–145.
ESAIM Control Optim. Calc. Var. 7 (2002), 285–289
Calc. Var. Partial Differential Equations 9 (1999), no. 4, 327–255.
OTHER
Comm. Partial Differential Equations 42 (2017), no. 10, 1510–1523.
Proc. IEEE Int. Symp. Inf. Th., Barcelona, Spain, Jul. 2016, pp. 2789-2793.
Comm. Pure Appl. Math. 62 (2009), no. 6, 789–830.
Comm. Partial Differential Equations 32 (2007), no. 1-3, 87–126.