Papers


new Fractional superharmonic functions and the Perron method for nonlinear integro-differential equations
(with J. Korvenpaa, and T. Kuusi), Math. Ann. (2016), 47pp.

26• A note on fractional supersolutions
(with J. Korvenpaa, and T. Kuusi), Electron. J. Differential Equations Vol. 2016 (2016), No. 263, 19.

25• Intrinsic geometry and De Giorgi classes certain anisotropic Sobolev spaces
(with P. Baroni and A. Di Castro), Discrete Contin. Dyn. Syst. Ser. S. 10 (2017), No. 4, 647–659.

24• The obstacle problem for nonlinear integro-differential operators
(with J. Korvenpaa, and T. Kuusi), Calc. Var. Partial Differential Equations 55 (2016), No. 3, Art. 63.

23• Holder regularity up to the boundary for a class of fractional obstacle problems
(with J. Korvenpaa, and T. Kuusi), Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 27 (2016), 355–367.

22• A Global Compactness type result for Palais-Smale sequences in fractional Sobolev spaces
(with A. Pisante), Nonlinear Anal. 117 (2015), 1–7. Highly-cited

21• Nonlocal Harnack inequalities
(with A. Di Castro and T. Kuusi), J. Funct. Anal. 267 (2014), No. 6, 1807–1836. Highly-cited

20• Local behavior of fractional p-minimizers
(with A. Di Castro and T. Kuusi), Ann. Inst. H. Poincaré Anal. Non Linéaire 33 (2016), 1279–1299. Highly-cited

19• Dislocation dynamics in crystals: a macroscopic theory in a fractional Laplace setting
(with S. Dipierro and E. Valdinoci), Comm. Math. Phys. 333 (2015), No. 2, 1061–1105.

18• Fractional p-eigenvalues
(with G. Franzina), Riv. Mat. Univ. Parma 5 (2014), No. 2, 315–328.

17• Improved Sobolev embeddings, profile decomposition, and concentration-compactness for fractional Sobolev spaces
(with A. Pisante), Calc. Var. Partial Differential Equations 50 (2014), No. 3-4, 799–829. Highly-cited

16• Subcritical approximation of Yamabe type nonlocal equation: a Gamma-convergence approach
(with A. Pisante, Y. Sire), Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) XIV (2015), 1–22.

15• Global estimates for nonlinear parabolic equations
(with P. Baroni and A. Di Castro), J. Evol. Equations 13 (2013), No. 1, 163–195.

14• Fractional regularity for nonlinear elliptic problems with measure data
(with A. Di Castro), J. Convex Anal. 20 (2013), No. 4, 901–918.

13• Asymptotics of the $s$-perimeter as $s\searrow0$
(with S. Dipierro, A. Figalli and E. Valdinoci), Discrete Contin. Dyn. Syst. 33 (2013), No. 7, 2777–2790.

12• Existence and symmetry results for a Schrödinger type problem involving the fractional Laplacian
(with S. Dipierro and E. Valdinoci), Le Matematiche 68 (2013), No. 1, 201–216.

11• Nonlinear parabolic problems with lower order terms and related integral estimates
(with A. Di Castro), Nonlinear Anal. 75 (2012), 4177–4197.

10• Measure data problems, lower order terms and interpolation effects
(with A. Di Castro), Ann. Mat. Pura Appl. 193 (2014), No. 2, 325-358.

hot Hitchhiker’s guide to the fractional Sobolev spaces
(with E. Di Nezza and E. Valdinoci), Bull. Sci. math. 136 (2012), No. 5, 521–573. Highly-cited

8• Local and Global minimizers for a variational energy involving a fractional norm
(with O. Savin and E. Valdinoci), Ann. Mat. Pura Appl. 192 (2013), No. 4, 673–718. Highly-cited

7• p-Laplacian problems with critical Sobolev exponent
Asymptotic Analysis 73 (2011), n. 1-2, 37–52.

6• A weighted gradient theory of phase transitions with a possibly singular and degenerate spatial inhomogeneity
(with E. Valdinoci), J. Differential Equations 252 (2012), 3381–3402.

5• Subcritical approximation of the Sobolev quotient and a related concentration result
Rend. Sem. Mat. Univ. Padova 125 (2011), 1–14.

4• $\Gamma$-Convergence of some super quadratic functionals with singular weights
(with Y. Sire), Math. Z. 266 (2010), n. 3, 533–560.

3• Phase transitions with the line tension effect: the super-quadratic case
Math. Models Methods Appl. Sci. (M3AS) 19 (2009), n. 10, 1765–1795.

2• Una classe di problemi di transizione di fase con l’effetto di tensione di linea
Matematica nella Società e nella Cultura: rivista dell’Unione Matematica Italiana, Serie I, Vol. I, N. 2 (2008), 323–326.

1• A singular perturbation result with a fractional norm
(with A. Garroni), Progress in NonLinear Differential Equations and their Applications 68 (2006), 111–126.

0• A class of phase transition problems with the line tension effect
Ph.D. Thesis, Università degli Studi di “Roma Tre”, 2007.


Posters and other works

pdf Asymptotics of the fractional Perimeter functionals
(with S. Dipierro), Recent advances in partial differential equations and applications, Milano, June 17-21, 2013.
Also in
SIAM@PoliMI, Politecnico di Milano, June 28, 2013.

Possibili approcci alle equazioni differenziali astratte di tipo parabolico (Italian)
Master Thesis, Supervisor: Prof. Claudio Baiocchi, Sapienza Università di Roma (Jul 2002).



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