@article {2013,
	title = {Dislocation dynamics in crystals: a macroscopic theory in a fractional Laplace setting},
	number = {SISSA preprint;43/2013/MATE},
	year = {2013},
	institution = {SISSA},
	abstract = {We consider an evolution equation arising in the Peierls-Nabarro model for crystal dislocation. We study the evolution of such dislocation function and show that, at a macroscopic scale, the dislocations have the tendency to concentrate at single points of the crystal, where the size of the slip coincides with the natural periodicity of the medium. These dislocation points evolve according to the external stress and an interior repulsive potential.},
	keywords = {nonlocal Allen-Cahn equation},
	url = {http://hdl.handle.net/1963/7124},
	author = {Serena Dipierro and Giampiero Palatucci and Enrico Valdinoci}
}
@article {2013,
	title = {Existence and symmetry results for a Schrodinger type problem  involving the fractional Laplacian},
	journal = {Le Matematiche (Catania), Vol. 68 (2013), no. 1: 201-216},
	number = {arXiv:1202.0576v1;},
	year = {2013},
	publisher = {University of Catania},
	abstract = {<p>This paper deals with the following class of nonlocal Schr\"odinger equations $$ \displaystyle (-\Delta)^s u + u = |u|^{p-1}u \ \ \text{in} \ \mathbb{R}^N, \quad \text{for} \ s\in (0,1). $$ We prove existence and symmetry results for the solutions $u$ in the fractional Sobolev space $H^s(\mathbb{R}^N)$. Our results are in clear accordance with those for the classical local counterpart, that is when $s=1$.</p>},
	author = {Serena Dipierro and Giampiero Palatucci and Enrico Valdinoci}
}
@article {2012,
	title = {Asymptotics of the s-perimeter as  s {\textrightarrow}0 },
	journal = {Discrete Contin. Dyn. Syst. 33, nr.7 (2012): 2777-2790},
	number = {arXiv:1204.0750v2;},
	year = {2012},
	publisher = {American Institute of Mathematical Sciences},
	abstract = {<p>We deal with the asymptotic behavior of the $s$-perimeter of a set $E$ inside a domain $\Omega$ as $s\searrow0$. We prove necessary and sufficient conditions for the existence of such limit, by also providing an explicit formulation in terms of the Lebesgue measure of $E$ and $\Omega$. Moreover, we construct examples of sets for which the limit does not exist.</p>},
	doi = {10.3934/dcds.2013.33.2777},
	author = {Serena Dipierro and Alessio Figalli and Giampiero Palatucci and Enrico Valdinoci}
}
@article {Berti2008601,
	title = {On periodic elliptic equations with gradient dependence},
	journal = {Communications on Pure and Applied Analysis},
	volume = {7},
	number = {3},
	year = {2008},
	note = {cited By (since 1996)1},
	pages = {601-615},
	abstract = {We construct entire solutions of Δu = f(x, u, ∇u) which are superpositions of odd, periodic functions and linear ones, with prescribed integer or rational slope.},
	issn = {15340392},
	author = {Massimiliano Berti and Matzeu, M and Enrico Valdinoci}
}
@article {2004,
	title = {Periodic orbits close to elliptic tori and applications to the three-body problem},
	journal = {Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 3 (2004) 87-138},
	number = {SISSA;28/2003/M},
	year = {2004},
	publisher = {Scuola Normale Superiore di Pisa},
	abstract = {We prove, under suitable non-resonance and non-degeneracy {\textquoteleft}{\textquoteleft}twist\\\'\\\' conditions, a Birkhoff-Lewis type result showing the existence of infinitely many periodic solutions, with larger and larger minimal period, accumulating onto elliptic invariant tori (of Hamiltonian systems). We prove the applicability of this result to the spatial planetary three-body problem in the small eccentricity-inclination regime. Furthermore, we find other periodic orbits under some restrictions on the period and the masses of the {\textquoteleft}{\textquoteleft}planets\\\'\\\'. The proofs are based on averaging theory, KAM theory and variational methods. (Supported by M.U.R.S.T. Variational Methods and Nonlinear Differential Equations.)},
	url = {http://hdl.handle.net/1963/2985},
	author = {Massimiliano Berti and Luca Biasco and Enrico Valdinoci}
}
