Papers


Preprint page on arXiv

  1. (with D. Fiorletta) An uncertainty principle for fractional operators, in preparation
  2. (with Z. Yin) Uniform resolvent estimates for magnetic operators, in preparation
  3. (with F. Cacciafesta, Z. Yin, J. Zhang) Dispersion estimates for Dirac equations in Aharonov-Bohm magnetic fields I: massless case, submitted
  4. (with A. Zanni) Scattering for the defocusing NLS on the line with variable coefficients, submitted
  5. (with T. A. Bui, X. T. Duong) On sharp estimates for Schröodinger groups of fractional powers of nonnegative self-adjoint operators, J. Differential Equations 381 (2024), 260-292.
  6. (with T. A. Bui) Generalized Hardy Operators, Nonlinearity 36 (2023), 171-198
  7. (with R. Schnaubelt) Global Strichartz estimates for an inhomogeneous Maxwell system, Communications in PDE 47 (2022), 630-675
  8. (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
  9. (with L. Fanelli, N. Schiavone) Eigenvalue bounds for non-selfadjoint Dirac operators, Math. Annalen 383 (2022), 621-644 (Open Access link)
  10. On the supercritical defocusing NLW outside a ball, Analysis and Mathematical Physics 11 (2021), Paper No. 141 (Open Access link)
  11. On the supercritical Schrödinger equation on the exterior of a ball, Communications in PDE 46 (2021) 1389-1409
  12. On large potential perturbations of the Schrödinger, wave and Klein--Gordon equations, Comm. Pure Appl. Anal. 19 (2020) 609-640
  13. (with T. A. Bui, F. Nicola) Sharp Lp estimates for Schrödinger groups on spaces of homogeneous type, Revista Mat. Iberoam 36 (2020) 455-484
  14. (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
  15. A short proof of commutator estimates, J. Fourier Anal. Appl. 25 (2019) 1134-1146
  16. (with S. Nicaise, R. Schnaubelt) Blow--up for nonlinear Maxwell equations, EJDE paper no.73 (2018) 1-9
  17. (with R.Lucà) Stability properties of the regular set for the Navier--Stokes equation, J. Math. Fluid Mech. 20 (2018) 819-852
  18. (with F.Cacciafesta, R.Lucà) A limiting absorption principle for the Helmholtz equation with variable coefficients, J. Spectral Theory 8 (2018) 1349-1392
  19. (with M. Okamoto) On the cubic Dirac equation with potential and the Lochak--Majorana condition, J. Math. Anal. Appl. 456 (2017) 1203-1237
  20. (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
  21. (with M. Okamoto) Blowup and ill-posedness results for the Dirac equation without gauge invariance, Evolution Equations and Control Theory 5 (2016) 225-234
  22. (with F.Cacciafesta, R.Lucà) Helmholtz and dispersive equations with variable coefficients on exterior domains, SIAM J. Math. Anal. 48 (2016) 1798-1832
  23. (with R.Lucà) On the regularity set and angular integrability for the Navier-Stokes equation, Arch. Ration. Mech. Anal. 221 (2016) 1255-1284
  24. (with F.Nicola) Sharp Lp estimates for Schrödinger groups, Rev. Mat. Iberoam. 32 (2016) 1019-1038
  25. (with B.Cassano) Scattering in the energy space for the NLS with variable coefficients, Math. Ann. 366 (2016) 479-543
  26. (with Q.Zhang) Global existence of small equivariant wave maps on rotationally symmetric manifolds, Int. Math. Res. Not. 4 (2016) 978-1025
  27. (with P.Maheux, V.Pierfelice) Log-Sobolev inequalities for semi-direct product operators and applications, Math. Z. 283 (2016) 103-131
  28. Kato smoothing and Strichartz estimates for wave equations with magnetic potentials, Comm. Math. Phys. 335 (2015) 1-16
  29. (with M.Cappiello and F.Nicola) On the radius of spatial analyticity for semilinear symmetric hyperbolic systems, J. Differential Equations 256 (2014) 2603-2618
  30. (with F.Cacciafesta) Endpoint estimates and global existence for the nonlinear Dirac equation with potential, J. Differential Equations 254 (2013) 2233-2260
  31. (with R.Racke) Evolution equations on non flat waveguides, Arch. Ration. Mech. Anal. 206 (2012) 81-110
  32. (with R.Lucà) Stein-Weiss and Caffarelli-Kohn-Nirenberg inequalities with angular integrabilityl, J. Math. Anal. Appl. 388 (2012) 1061-1079
  33. (with S.Selberg) Dispersive estimates for the 1D Schrödinger equation with a steplike potential, J. Differential Equations 252 (2012) 1603-1634
  34. (with S.Selberg) Global well-posedness of the Maxwell-Dirac system in two space dimensions, J. Funct. Anal. 260 (2011) 2300-2365
  35. (with F.Cacciafesta) Weighted Lp estimates for powers of selfadjoint operators, Adv. Math. 229 (2012) 501-530
  36. (with D.Foschi, S.Selberg) Product estimates for wave-Sobolev spaces in 2 + 1 and 1 + 1 dimensions, Contemp. Math. 526 (2010) 125-150
  37. (with N.Boussaid, L.Fanelli) Smoothing estimates for the Dirac equation with a magnetic potential, J. Math. Pures Appl. 95 (2011) 137-150
  38. (with D.Foschi, S.Selberg) Atlas of products for wave-Sobolev spaces, Trans. Amer. Math. Soc. 364 (2012) 31-63
  39. (with L.Fanelli, L.Vega, N.Visciglia) Endpoint Strichartz estimates for the magnetic Schrödinger equation, J. Funct. Anal. 258 (2010) 3227-3240
  40. (with L.Fanelli) Smoothing estimates for the Schrödinger equation with unbounded potentials, J. Differential Equations 246 (2009) 4552-4567
  41. (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
  42. (with D.Foschi, S.Selberg) Null structure and local well-posedness of the Maxwell-Dirac system, Amer. J. Math. 132 (2010) 771-839
  43. (with T.Kinoshita, S.Spagnolo) On the 2 by 2 weakly hyperbolic systems, Osaka J. Math. 45 (2008) 921-939
  44. (with L.Fanelli) Strichartz and smoothing estimates for dispersive equations with magnetic potentials, Comm. Partial Differential Equations 33 (6) (2008) 1082-1112
  45. (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
  46. (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
  47. (with L.Fanelli) Lp - boundedness of the wave operator for the one dimensional Schrödinger operator, Comm. Math. Phys. 268 (2006) 415-438
  48. (with L.Fanelli) Decay estimates for the wave and Dirac equations with a magnetic potential, Comm. Pure Appl. Math. 60 (2007) 357-392
  49. (with V.Pierfelice, S.Teta) Dispersive estimate for the Schrödinger equation with point interactions, Math. Methods Appl. Sci. 29 (2006) 309-323
  50. (with V.Pierfelice, N.Visciglia) Some remarks on the Schrödinger equation with a potential in Lrt Lsx, Math. Ann. 333 (2005) 271-290
  51. (with V.Pierfelice) On the wave equation with a large rough potential, J. Funct. Anal. 227 (2005), 30-77
  52. (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)
  53. 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
  54. (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
  55. (with V.Georgiev) Stability of solitary waves for the Maxwell-Schrödinger equation with external Coulomb potential: electrostatic case. (Fourth ISAAC Congress, Toronto, 2003)
  56. (with V.Georgiev) On the continuity of the solution operator to the wave map system, Comm. Pure Appl. Math. 57 (2004), 357-383 (ArXiv)
  57. (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
  58. (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
  59. (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
  60. (with V.Georgiev) Low regularity solutions for the wave map equation into the 2-D sphere, Math. Z. 248 (2004), 227-266 (.pdf file)
  61. (with T.Kinoshita, S.Spagnolo) Weakly hyperbolic systems with Hoelder continuous coefficients, J. Diff. Equations 203 (2004) 64-81 (.pdf file)
  62. (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)
  63. (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
  64. (with P.Trebeschi) On the local solvability for a nonlinear weakly hyperbolic equation with analytic coefficients, Comm. Partial Differential Equations 26 (2001) 779-811
  65. (with M.Di Flaviano) On a weakly hyperbolic quasilinear mixed problem of second order Annali Scu. Norm. Sup. Pisa 30 (2001), 251-267
  66. (with V.Georgiev, H.Kubo) Weighted Strichartz estimates for the wave equation, Comptes Rendus Acad. Sci. Paris 330 (2000), 349-354
  67. (with S.Spagnolo) A remark on uniformly symmetrizable systems. Advances in Math. 158 (2001), 18-25 (.pdf file)
  68. (with V.Georgiev, H.Kubo) Weighted decay estimates for the wave equation, J. Diff. Equations 177 (2001), 146-200
  69. (with V.Georgiev, H.Kubo) Weighted Strichartz estimate for the wave equation, Comptes Rendus Acad. Sci. Paris 330 (2000), 349-354
  70. (with M.Di Flaviano) An abstract degenerate hyperbolic equation with application to mixed problems, Hokkaido Math. J. 29 (2000), 315-328
  71. (with A.Di Giuseppe) Global existence with large data for a nonlinear weakly hyperbolic equation, Math. Nachr. 231 (2001), 5-23
  72. (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
  73. (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
  74. (with R.Racke) Weakly hyperbolic equations in domains with boundaries, Nonlinear Anal. 33 (1998), 455-472
  75. (with M.DiFlaviano) On quasilinear hyperbolic equations with degenerate principal part, Tsukuba J. Math. 22 (1998), 559-574
  76. (with S.Spagnolo) Quasi-symmetrization of hyperbolic systems and propagation of the analytic regularity, Boll. Unione Mat. Ital. 1-B (1998), 169-185
  77. (with S.Spagnolo) The Cauchy Problem for Weakly Parabolic Systems, Math.Ann. 309 (1997), 307-330
  78. (with S.Spagnolo) Small analytic solutions to nonlinear weakly hyperbolic systems, Ann. Sc. Norm. Super. Pisa Cl. Sci. IV.22 (1995), 469-491
  79. A note on a theorem of Joergens, Math. Z. 218 (1995), 239-252
  80. (with S.Spagnolo) Kirchhoff type equations depending on a small parameter, Chinese Ann. Math. 16B (1995), 413-430
  81. (with Y.Shibata) On global solvability of nonlinear viscoelastic equations in the analytic category, Math. Methods Appl. Sci. 17 (1994), 477-486
  82. The Cauchy problem for semilinear weakly hyperbolic equations in Hilbert spaces, Ann. Inst. Henri Poincaré Anal. Non Linéaire 11 (1994), 343-358
  83. On weakly hyperbolic equations in Hilbert spaces, Funkcial. Ekvac. 38 (1995), 159-177
  84. (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
  85. (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
  86. (with R.Manfrin) A class of locally solvable semilinear equations of weakly hyperbolic type, Ann. Mat. Pura Appl. 168 (1995), 355-372
  87. On a semilinear weakly hyperbolic equation with logarithmic nonlinearity, Differ. Int. Equations 7 (1994), 121-132
  88. (with S.Spagnolo) Nonlinear perturbations of the Kirchhoff equation, Comm. Pure Appl. Math. 47 (1994), 1005-1029
  89. Local existence for semilinear weakly hyperbolic equations with time dependent coefficients, Nonlin. Analysis T.M.A. 21 (1993), 685-696
  90. (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
  91. (with S.Spagnolo) A class of nonlinear hyperbolic problems with global solutions, Arch. Ration. Mech. and Anal. 124 (1993), 201-219
  92. (with L.Ambrosio, S.Mortola) Gamma-convergence and the least square method, Ann. Mat. Pura Appl. 166 (1994), 101-127
  93. Well posedness in C∞ for a weakly hyperbolic second order equation, Rend. Sem. Mat. Univ. Padova 91 (1994), 65-83
  94. (with S.Spagnolo) Global solvability for the degenerate Kirchhoff equation with real analytic data, Invent. Math. 108 (1992), 247-262
  95. Periodic solutions for a second order partial differential equation, Ann. Sc. Norm. Super. Pisa Cl. Sci. 19 (1992), 493-506
  96. (with Bernard Gaveau) The singularity of the fundamental solution of certain hyperbolic systems, Pubbl. Dip. Mat. Univ. Pisa 2.52 (551) (1990)
  97. (with Andrea D'Agnolo, Giuseppe Zampieri) Extension of CR functions to "wedge type" domains, Rend. Mat. Acc. Lincei IX.2 (1991), 35-42
  98. (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
  99. (with Sergio Spagnolo) On the life span of the analytic solutions to quasilinear weakly hyperbolic equations, Indiana Univ. Math. J. 40 (1991), 71-98
  100. (with Nobuyuki Tose, Giuseppe Zampieri) Propagation of singularities up to the boundary along leaves, Comm. Partial Differential Equations 15 (1990), 453-460
  101. (with Andrea Braides) Perimeter on fractal sets, Manuscripta Math. 72 (1991), 5-25
  102. Gevrey well-posedness of an abstract Cauchy problem of weakly hyperbolic type, Publ. RIMS Kyoto 24 (1988), 433-449
  103. 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)