Preprint page on arXiv

  1. (with F. Cacciafesta, J. Zhang) Dispersion estimates for Dirac equations in Aharonov-Bohm magnetic fields I: massless case, in preparation
  2. (with A. Zanni) Blow up alternative for the focusing NLS on the line with variable coefficients, in preparation
  3. (with A. Zanni) Scattering for the defocusing NLS on the line with variable coefficients, submitted
  4. (with T. A. Bui, X. T. Duong) On sharp estimates for Schröodinger groups of fractional powers of nonnegative self-adjoint operators, submitted
  5. (with T. A. Bui) Generalized Hardy Operators, Nonlinearity 36 (2023), 171-198
  6. (with R. Schnaubelt) Global Strichartz estimates for an inhomogeneous Maxwell system, Communications in PDE 47 (2022), 630-675
  7. (with L. Fanelli, D. Krejčiřík, N. Schiavone) Localization of eigenvalues for non-self-adjoint Dirac and Klein-Gordon operators, Nonlinear Analysis 214 (2022), Paper No. 112565
  8. (with L. Fanelli, N. Schiavone) Eigenvalue bounds for non-selfadjoint Dirac operators, Math. Annalen 383 (2022), 621-644 (Open Access link)
  9. On the supercritical defocusing NLW outside a ball, Analysis and Mathematical Physics 11 (2021), Paper No. 141 (Open Access link)
  10. On the supercritical Schrödinger equation on the exterior of a ball, Communications in PDE 46 (2021) 1389-1409
  11. On large potential perturbations of the Schrödinger, wave and Klein--Gordon equations, Comm. Pure Appl. Anal. 19 (2020) 609-640
  12. (with T. A. Bui, F. Nicola) Sharp Lp estimates for Schrödinger groups on spaces of homogeneous type, Revista Mat. Iberoam 36 (2020) 455-484
  13. (with T. A. Bui, X. T. Duong, D. Müller) On the flows associated to selfadjoint operators on metric measure spaces, Mathematische Annalen 375 (2019) 1393-1426
  14. A short proof of commutator estimates, J. Fourier Anal. Appl. 25 (2019) 1134-1146
  15. (with S. Nicaise, R. Schnaubelt) Blow--up for nonlinear Maxwell equations, EJDE paper no.73 (2018) 1-9
  16. (with R.Lucà) Stability properties of the regular set for the Navier--Stokes equation, J. Math. Fluid Mech. 20 (2018) 819-852
  17. (with F.Cacciafesta, R.Lucà) A limiting absorption principle for the Helmholtz equation with variable coefficients, J. Spectral Theory 8 (2018) 1349-1392
  18. (with M. Okamoto) On the cubic Dirac equation with potential and the Lochak--Majorana condition, J. Math. Anal. Appl. 456 (2017) 1203-1237
  19. (with T. A. Bui, X. T. Duong, J. Li, F. K. Ly) Weighted estimates for powers and smoothing estimates of Schrödinger operators with inverse-square potentials, J. Differential Equations 262 (2017) 2771-2807
  20. (with M. Okamoto) Blowup and ill-posedness results for the Dirac equation without gauge invariance, Evolution Equations and Control Theory 5 (2016) 225-234
  21. (with F.Cacciafesta, R.Lucà) Helmholtz and dispersive equations with variable coefficients on exterior domains, SIAM J. Math. Anal. 48 (2016) 1798-1832
  22. (with R.Lucà) On the regularity set and angular integrability for the Navier-Stokes equation, Arch. Ration. Mech. Anal. 221 (2016) 1255-1284
  23. (with F.Nicola) Sharp Lp estimates for Schrödinger groups, Rev. Mat. Iberoam. 32 (2016) 1019-1038
  24. (with B.Cassano) Scattering in the energy space for the NLS with variable coefficients, Math. Ann. 366 (2016) 479-543
  25. (with Q.Zhang) Global existence of small equivariant wave maps on rotationally symmetric manifolds, Int. Math. Res. Not. 4 (2016) 978-1025
  26. (with P.Maheux, V.Pierfelice) Log-Sobolev inequalities for semi-direct product operators and applications, Math. Z. 283 (2016) 103-131
  27. Kato smoothing and Strichartz estimates for wave equations with magnetic potentials, Comm. Math. Phys. 335 (2015) 1-16
  28. (with M.Cappiello and F.Nicola) On the radius of spatial analyticity for semilinear symmetric hyperbolic systems, J. Differential Equations 256 (2014) 2603-2618
  29. (with F.Cacciafesta) Endpoint estimates and global existence for the nonlinear Dirac equation with potential, J. Differential Equations 254 (2013) 2233-2260
  30. (with R.Racke) Evolution equations on non flat waveguides, Arch. Ration. Mech. Anal. 206 (2012) 81-110
  31. (with R.Lucà) Stein-Weiss and Caffarelli-Kohn-Nirenberg inequalities with angular integrabilityl, J. Math. Anal. Appl. 388 (2012) 1061-1079
  32. (with S.Selberg) Dispersive estimates for the 1D Schrödinger equation with a steplike potential, J. Differential Equations 252 (2012) 1603-1634
  33. (with S.Selberg) Global well-posedness of the Maxwell-Dirac system in two space dimensions, J. Funct. Anal. 260 (2011) 2300-2365
  34. (with F.Cacciafesta) Weighted Lp estimates for powers of selfadjoint operators, Adv. Math. 229 (2012) 501-530
  35. (with D.Foschi, S.Selberg) Product estimates for wave-Sobolev spaces in 2 + 1 and 1 + 1 dimensions, Contemp. Math. 526 (2010) 125-150
  36. (with N.Boussaid, L.Fanelli) Smoothing estimates for the Dirac equation with a magnetic potential, J. Math. Pures Appl. 95 (2011) 137-150
  37. (with D.Foschi, S.Selberg) Atlas of products for wave-Sobolev spaces, Trans. Amer. Math. Soc. 364 (2012) 31-63
  38. (with L.Fanelli, L.Vega, N.Visciglia) Endpoint Strichartz estimates for the magnetic Schrödinger equation, J. Funct. Anal. 258 (2010) 3227-3240
  39. (with L.Fanelli) Smoothing estimates for the Schrödinger equation with unbounded potentials, J. Differential Equations 246 (2009) 4552-4567
  40. (with V.Pierfelice, F.Ricci) On the wave equation associated to the Hermite and the twisted Laplacian, J. Fourier Anal. Appl. 16 (2010) 294-310
  41. (with D.Foschi, S.Selberg) Null structure and local well-posedness of the Maxwell-Dirac system, Amer. J. Math. 132 (2010) 771-839
  42. (with T.Kinoshita, S.Spagnolo) On the 2 by 2 weakly hyperbolic systems, Osaka J. Math. 45 (2008) 921-939
  43. (with L.Fanelli) Strichartz and smoothing estimates for dispersive equations with magnetic potentials, Comm. Partial Differential Equations 33 (6) (2008) 1082-1112
  44. (with D.Foschi, S.Selberg) Local well-posedness below the charge norm for the Dirac-Klein-Gordon system in two space dimensions, J. Hyperbolic Differ. Equ. 4 (2007) 1-36
  45. (with D.Foschi, S.Selberg) Null structure and almost optimal local well-posedness of the Dirac-Klein-Gordon system, J. Eur. Math. Soc. 9 (2007) 877-899
  46. (with L.Fanelli) Lp - boundedness of the wave operator for the one dimensional Schrödinger operator, Comm. Math. Phys. 268 (2006) 415-438
  47. (with L.Fanelli) Decay estimates for the wave and Dirac equations with a magnetic potential, Comm. Pure Appl. Math. 60 (2007) 357-392
  48. (with V.Pierfelice, S.Teta) Dispersive estimate for the Schrödinger equation with point interactions, Math. Methods Appl. Sci. 29 (2006) 309-323
  49. (with V.Pierfelice, N.Visciglia) Some remarks on the Schrödinger equation with a potential in Lrt Lsx, Math. Ann. 333 (2005) 271-290
  50. (with V.Pierfelice) On the wave equation with a large rough potential, J. Funct. Anal. 227 (2005), 30-77
  51. (with E.Montefusco) Il dubbio di Didone. Ricordando Franco Conti, 59-79, Pubbl. Cent. Ric. Mat. Ennio Giorgi, Scuola Norm. Sup., Pisa, 2004 (.pdf file)
  52. Instability for geometric wave equations. Phase space analysis of partial differential equations. Vol. I, 155-174, Pubbl. Cent. Ric. Mat. Ennio Giorgi, Scuola Norm. Sup., Pisa, 2004
  53. (with V.Georgiev) Wave maps and ill posedness of their Cauchy problem. New trends in the theory of hyperbolic equations, 1-111, Oper. Theory Adv. Appl. 159, Birkhauser, Basel, 2005
  54. (with V.Georgiev) Stability of solitary waves for the Maxwell-Schrödinger equation with external Coulomb potential: electrostatic case. (Fourth ISAAC Congress, Toronto, 2003)
  55. (with V.Georgiev) On the continuity of the solution operator to the wave map system, Comm. Pure Appl. Math. 57 (2004), 357-383 (ArXiv)
  56. (with V.Georgiev) Recent ill-posedness results for the wave map system in critical spaces. Hyperbolic problems and related topics (Cortona, 2002), 137-146, Grad. Ser. Anal., Int. Press, Somerville, MA, 2003
  57. (with V.Georgiev) Ill posedness for the 2-D wave map equation. Progress in analysis, Vol. I, II (Third ISAAC congress, Berlin, 2001), 913-931, World Sci. Publishing, River Edge, NJ, 2003
  58. (with V.Georgiev) On Lipschitz continuity of the solution map for two dimensional wave maps. Evolution equations (Warsaw, 2001), 95-103, Banach Center Publ. 60, Polish Acad. Sci., Warsaw, 2003
  59. (with V.Georgiev) Low regularity solutions for the wave map equation into the 2-D sphere, Math. Z. 248 (2004), 227-266 (.pdf file)
  60. (with T.Kinoshita, S.Spagnolo) Weakly hyperbolic systems with Hoelder continuous coefficients, J. Diff. Equations 203 (2004) 64-81 (.pdf file)
  61. (with T.Kinoshita) On the wellposedness of the Cauchy problem for weakly hyperbolic equations of higher order, Math. Nachr. 278 (2005) 1147-1162 (.pdf file)
  62. (with T.Kinoshita) On the wellposedness of the Cauchy problem for weakly hyperbolic equations of higher order. Microlocal analysis and related topics (Japanese) (Kyoto, 2001). Surikaisekikenkyusho Kokyuroku 1261 (2002) 46-55
  63. (with P.Trebeschi) On the local solvability for a nonlinear weakly hyperbolic equation with analytic coefficients, Comm. Partial Differential Equations 26 (2001) 779-811
  64. (with M.Di Flaviano) On a weakly hyperbolic quasilinear mixed problem of second order Annali Scu. Norm. Sup. Pisa 30 (2001), 251-267
  65. (with V.Georgiev, H.Kubo) Weighted Strichartz estimates for the wave equation, Comptes Rendus Acad. Sci. Paris 330 (2000), 349-354
  66. (with S.Spagnolo) A remark on uniformly symmetrizable systems. Advances in Math. 158 (2001), 18-25 (.pdf file)
  67. (with V.Georgiev, H.Kubo) Weighted decay estimates for the wave equation, J. Diff. Equations 177 (2001), 146-200
  68. (with V.Georgiev, H.Kubo) Weighted Strichartz estimate for the wave equation, Comptes Rendus Acad. Sci. Paris 330 (2000), 349-354
  69. (with M.Di Flaviano) An abstract degenerate hyperbolic equation with application to mixed problems, Hokkaido Math. J. 29 (2000), 315-328
  70. (with A.Di Giuseppe) Global existence with large data for a nonlinear weakly hyperbolic equation, Math. Nachr. 231 (2001), 5-23
  71. (with S.Spagnolo) On pseudosymmetric hyperbolic systems, Ann. Sc. Norm. Super. Pisa Cl. Sci. 25 (1997), 397-417, Volume in memoria di Ennio De Giorgi
  72. (with M.Reissig) New trends in the theory of nonlinear weakly hyperbolic equations of second order, Proceedings of the Second World Congress of Nonlinear Analysts, Part 4 (Athens 1996), Nonlinear Anal. 30 (1997), 2507-2515
  73. (with R.Racke) Weakly hyperbolic equations in domains with boundaries, Nonlinear Anal. 33 (1998), 455-472
  74. (with M.DiFlaviano) On quasilinear hyperbolic equations with degenerate principal part, Tsukuba J. Math. 22 (1998), 559-574
  75. (with S.Spagnolo) Quasi-symmetrization of hyperbolic systems and propagation of the analytic regularity, Boll. Unione Mat. Ital. 1-B (1998), 169-185
  76. (with S.Spagnolo) The Cauchy Problem for Weakly Parabolic Systems, Math.Ann. 309 (1997), 307-330
  77. (with S.Spagnolo) Small analytic solutions to nonlinear weakly hyperbolic systems, Ann. Sc. Norm. Super. Pisa Cl. Sci. IV.22 (1995), 469-491
  78. A note on a theorem of Joergens, Math. Z. 218 (1995), 239-252
  79. (with S.Spagnolo) Kirchhoff type equations depending on a small parameter, Chinese Ann. Math. 16B (1995), 413-430
  80. (with Y.Shibata) On global solvability of nonlinear viscoelastic equations in the analytic category, Math. Methods Appl. Sci. 17 (1994), 477-486
  81. The Cauchy problem for semilinear weakly hyperbolic equations in Hilbert spaces, Ann. Inst. Henri Poincaré Anal. Non Linéaire 11 (1994), 343-358
  82. On weakly hyperbolic equations in Hilbert spaces, Funkcial. Ekvac. 38 (1995), 159-177
  83. (with R.Manfrin) The Cauchy problem in abstract Gevrey spaces for a nonlinear weakly hyperbolic equation of second order, Hokkaido Math. J. 23 (1994), 119-141
  84. (with R.Manfrin) Sufficient conditions for the local solvability of some quasilinear equations of weakly hyperbolic type, Boll. Unione Mat. Ital. (7)8-B (1994), 731-754
  85. (with R.Manfrin) A class of locally solvable semilinear equations of weakly hyperbolic type, Ann. Mat. Pura Appl. 168 (1995), 355-372
  86. On a semilinear weakly hyperbolic equation with logarithmic nonlinearity, Differ. Int. Equations 7 (1994), 121-132
  87. (with S.Spagnolo) Nonlinear perturbations of the Kirchhoff equation, Comm. Pure Appl. Math. 47 (1994), 1005-1029
  88. Local existence for semilinear weakly hyperbolic equations with time dependent coefficients, Nonlin. Analysis T.M.A. 21 (1993), 685-696
  89. (with S.Spagnolo) On an abstract weakly hyperbolic equation modelling the nonlinear vibrating string, in: Developments in Partial Differential Equations and applications to Mathematical Physics (Ferrara 1991), G.Buttazzo and G.P.Galdi eds., Plenum Press, 1992, 27-32
  90. (with S.Spagnolo) A class of nonlinear hyperbolic problems with global solutions, Arch. Ration. Mech. and Anal. 124 (1993), 201-219
  91. (with L.Ambrosio, S.Mortola) Gamma-convergence and the least square method, Ann. Mat. Pura Appl. 166 (1994), 101-127
  92. Well posedness in C for a weakly hyperbolic second order equation, Rend. Sem. Mat. Univ. Padova 91 (1994), 65-83
  93. (with S.Spagnolo) Global solvability for the degenerate Kirchhoff equation with real analytic data, Invent. Math. 108 (1992), 247-262
  94. Periodic solutions for a second order partial differential equation, Ann. Sc. Norm. Super. Pisa Cl. Sci. 19 (1992), 493-506
  95. (with Bernard Gaveau) The singularity of the fundamental solution of certain hyperbolic systems, Pubbl. Dip. Mat. Univ. Pisa 2.52 (551) (1990)
  96. (with Andrea D'Agnolo, Giuseppe Zampieri) Extension of CR functions to "wedge type" domains, Rend. Mat. Acc. Lincei IX.2 (1991), 35-42
  97. (with Bernard Gaveau) Singularité de la solution fondamentale de certains systèmes hyperboliques à coefficients constants, C. R. Acad. Sci. Paris 310 (Série I) (1990), 757-760
  98. (with Sergio Spagnolo) On the life span of the analytic solutions to quasilinear weakly hyperbolic equations, Indiana Univ. Math. J. 40 (1991), 71-98
  99. (with Nobuyuki Tose, Giuseppe Zampieri) Propagation of singularities up to the boundary along leaves, Comm. Partial Differential Equations 15 (1990), 453-460
  100. (with Andrea Braides) Perimeter on fractal sets, Manuscripta Math. 72 (1991), 5-25
  101. Gevrey well-posedness of an abstract Cauchy problem of weakly hyperbolic type, Publ. RIMS Kyoto 24 (1988), 433-449
  102. Global solution of the Cauchy problem for a class of abstract nonlinear hyperbolic equations, Ann. Mat. Pura Appl. (IV) 130 (1988), 17-38

Erdős number = 3 (Erdős -> Kac -> Gaveau -> D'Ancona)