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