Associate Professor, Sapienza Università di Roma

Email: william.borrelli AT polimi.it

Available papers (27):

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• W. Borrelli - U. Morellini (preprint)
  The Pauli-Villars-regularized Dirac vacuum in electromagnetic fields at positive temperature (2026)
• W. Borrelli - R. Wu (Submitted Paper: J. Geom. Anal.)
  On the nodal set of solutions to Dirac equations (2026)
• W. Borrelli - P. Carimati - D. Fermi (J. Math. Anal. Appl.)
  On two-dimensional Dirac operators with critical delta-shell interactions (2026)
• W. Borrelli - U. Morellini (J. Phys. A: Math. Theor.)
  Global well-posedness in a Hartree-Fock model for graphene (2025)
• W. Borrelli - E. Danesi - S. Dovetta - L. Tentarelli (preprint)
  Dirac solitons in one-dimensional nonlinear Schrödinger equations (2025)
• W. Borrelli - M. Correggi - D. Fermi (Accepted Paper: J. Spectr. Theory)
  Pauli Hamiltonians with an Aharonov-Bohm flux (2024)
• W. Borrelli - A. Maalaoui - V. Martino (Calc. Var. PDE)
  Conformal Dirac-Einstein equations on manifolds with boundary (2023)
• W. Borrelli - N. Kerraoui - T. Ourmieres-Bonafos (Quantum Mathematics I - Springer Indam Series)
  Spectral asymptotics for two-dimensional Dirac operators in thin waveguides (2023)
• W. Borrelli (NoDEA Nonlinear Differential Equations Appl.)
  On the continuum limit for a model of binary waveguide arrays (2022)
• W. Borrelli - P. Briet - D. Krejcirik - T. Ourmieres-Bonafos (Ann. Henri Poincaré)
  Spectral properties of relativistic quantum waveguides (2022)
• W. Borrelli - S. J. N. Mosconi - M. Squassina (Rendiconti Lincei - Matematica e Applicazioni)
  Uniqueness of the critical point for solutions to some p-Laplace equations in the plane (2022)
• W. Borrelli - R. Carlone - L. Tentarelli (Comm. Math. Phys.)
  Complete ionization for a non-autonomous point interaction model in d=2 (2022)
• W. Borrelli - A. Malchiodi - R. Wu (Commun. Math. Phys.)
  Ground state Dirac bubbles and Killing spinors (2021)
• W. Borrelli - V. De Falco (Phys. Rev. D)
  Detection of chaos in the general relativistic Poynting-Robertson effect: Kerr equatorial plane (2021)
• W. Borrelli - R. Carlone (Proceedings: Nanosystems: Physics, Chemistry, Mathematics)
  Bifurcating standing waves for effective equations in gapped honeycomb structures (2021)
• W. Borrelli (Commun. Contemp. Math.)
  Symmetric solutions for a 2D critical Dirac equation (2021)
• W. Borrelli - V. De Falco (Phys. Rev. D)
  Timescales of the chaos onset in the general relativistic Poynting-Robertson effect (2021)
• W. Borrelli - R. Carlone - L. Tentarelli (J. Differential Equations)
  On the nonlinear Dirac equation on noncompact metric graphs (2021)
• W. Borrelli - R. Carlone - L. Tentarelli (Springer INdAM Series)
  A note on the Dirac operator with Kirchoff-type vertex conditions on noncompact metric graphs (2021)
• W. Borrelli - S. J. N. Mosconi - M. Squassina (Adv. Calc. Var.)
  Concavity properties for solutions to $p$-Laplace equations with concave nonlinearities (2021)
• W. Borrelli - R. L. Frank (Trans. Amer. Math. Soc.)
  Sharp decay estimates for critical Dirac equations (2020)
• W. Borrelli - A. Maalaoui (J. Geom. Anal.)
  Some properties of Dirac-Einstein bubbles (2020)
• W. Borrelli - R. Carlone - L. Tentarelli (SIAM J. Math. Anal.)
  Nonlinear Dirac Equation On Graphs With Localized Nonlinearities: Bound States And Nonrelativistic Limit (2019)
• W. Borrelli - R. Carlone - L. Tentarelli (Symmetry)
  An overview on the standing waves of nonlinear Schrödinger and Dirac equations on metric graphs with localized nonlinearity (2019)
• W. Borrelli (Journal of Mathematical Physics)
  Multiple solutions for a self-consistent Dirac equation in two dimensions (2018)
• W. Borrelli (Calc. Var. Partial Differential Equations)
  Weakly localized states for nonlinear Dirac equations (2018)
• W. Borrelli (Published paper: Journal of Differential Equations)
  Stationary solutions for the 2D critical Dirac equation with Kerr nonlinearity (2017)

Seminars:

• 3 jun 2019: Qualitative properties of critical Dirac equations

Speaker:

• 4 jul 2022 - 8 jul 2022: Summer School in Analysis and PDE

Organizer:

• 9 jun 2025 - 13 jun 2025: Analytical Methods in Quantum and Classical Mechanics
• 29 nov 2021 - 3 dec 2021: Winter school: "Analytical Methods in Quantum and Continuum Mechanics"