Research papers

• Global gradient regularity and a Hopf lemma for quasilinear operators of mixed local-nonlocal type
  C. A. Antonini, M. Cozzi
  submitted preprint. pdf
  
  
• A quantitative version of the Gidas-Ni-Nirenberg Theorem
  G. Ciraolo, M. Cozzi, M. Perugini, L. Pollastro
  submitted preprint. pdf
  
  
• Non-uniqueness for the nonlocal Liouville equation in  \( { \mathbb{R} } \) and applications
  L. Battaglia, M. Cozzi, A. J. Fernández, A. Pistoia
  SIAM J. Math. Anal. 55 (2023), no. 5, 4816-4842. pdf - journal
  
  
• Blowing-up solutions for a nonlocal Liouville type equation
  M. Cozzi, A. J. Fernández
  to appear in Ann. Sc. Norm. Super. Pisa Cl. Sci. (5). pdf - journal
  
  
• A fractional Michael-Simon Sobolev inequality on convex hypersurfaces
  X. Cabré, M. Cozzi, G. Csató
  Ann. Inst. H. Poincaré Anal. Non Linéaire 40 (2023), no. 3, 185-214. pdf - journal
  
  
• On nonlocal minimal graphs
  M. Cozzi, L. Lombardini
  Calc. Var. Partial Differential Equations 60 (2021), article no. 136, 72 pp. pdf​ - journal
  
  
• An elliptic boundary value problem with fractional nonlinearity
  N. Abatangelo, M. Cozzi
  SIAM J. Math. Anal. 53 (2021), no. 3, 3577-3601. pdf​ - journal
  
  
• A Bernstein-Moser-type result for nonlocal minimal graphs
  M. Cozzi, A. Farina, L. Lombardini
  Comm. Anal. Geom. 29 (2021), no. 4, 761-777. pdf - journal
  
  
• Long-time asymptotics for evolutionary crystal dislocation models
  M. Cozzi, J. Dávila, M. del Pino
  Adv. Math. 371 (2020), 107242, 109 pp. pdf​ - journal
  
  
• On the growth of nonlocal catenoids
  M. Cozzi, E. Valdinoci
  Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 31 (2020), no. 1, 237-248. pdf - journal
  
  
• A gradient estimate for nonlocal minimal graphs
  ​X. Cabré, M. Cozzi
  Duke Math. J. 168 (2019), no. 5, 775-848. pdf​ - journal
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• Planelike minimizers of nonlocal Ginzburg-Landau energies and fractional perimeters in periodic media
  M. Cozzi, E. Valdinoci
  Nonlinearity 31 (2018), no.7, 3013-3056. pdf - journal
  
  
• Regularity results and Harnack inequalities for minimizers and solutions of nonlocal problems: a unified approach via fractional De Giorgi classes
  M. Cozzi
  J. Funct. Anal. 272 (2017), no. 11, 4762-4837. pdf - journal
  
  
• Planelike interfaces in long-range Ising models and connections with nonlocal minimal surfaces
  M. Cozzi, S. Dipierro, E. Valdinoci
  J. Stat. Phys. 167 (2017), no. 6, 1401-1451. pdf - journal
  
  
• Plane-like minimizers for a non-local Ginzburg-Landau-type energy in a periodic medium
  M. Cozzi, E. Valdinoci
  J. Éc. polytech. Math. 4 (2017), 337-388. pdf - journal
  
  
• Interior regularity of solutions of non-local equations in Sobolev and Nikol'skii spaces
  M. Cozzi
  Ann. Mat. Pura Appl. 196 (2017), no. 2, 555-578. pdf - journal
  
  
• Monotonicity formulae and classification results for singular, degenerate, anisotropic PDEs
  M. Cozzi, A. Farina, E. Valdinoci
  Adv. Math. 293 (2016), 343-381. pdf - journal
  
  
• One-dimensional solutions of non-local Allen-Cahn-type equations with rough kernels
  M. Cozzi, T. Passalacqua
  J. Differential Equations 260 (2016), no. 8, 6638-6696. pdf - journal
  
  
• On the variation of the fractional mean curvature under the effect of  \( { \small C^{1,\alpha} } \) perturbations
  M. Cozzi
  Discrete Cont. Dyn. Syst. 35 (2015), no. 12, 5769-5786. pdf - journal
  
  
• Gradient bounds and rigidity results for singular, degenerate, anisotropic partial differential equations
  M. Cozzi, A. Farina, E. Valdinoci
  ​Comm. Math. Phys. 331 (2014), no. 1, 189-214. pdf - journal

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    Survey papers and lecture notes

• Fractional De Giorgi classes and applications to nonlocal regularity theory
  M. Cozzi
  Contemporary Research in elliptic PDEs and related topics​, 277-299
  Springer-INdAM Series, Vol. 33, Springer, Cham, 2019. pdf - chapter
  
  
• Regularity theory for local and nonlocal minimal surfaces: an overview
  M. Cozzi, A. Figalli
  Nonlocal and nonlinear diffusions and interactions: new methods and directions​, 117-158
  Lecture Notes in Math., Vol. 2186, CIME Found. Subser., Springer, 2017. pdf - chapter
  
  
• Nonlocal phase transitions in homogeneous and periodic media
  M. Cozzi, S. Dipierro, E. Valdinoci
  ​J. Fixed Point Theory Appl. 19 (2017), no. 1, 387-405. pdf - journal