A. Farina, E. Valdinoci: Geometry of quasiminimal phase transitions Calc. Var. Partial Differential Equations (Accepted Paper) 2007 M. Novaga, E. Valdinoci: The geometry of mesoscopic phase transition interfaces Discrete Contin. Dyn. Syst. Vol. 19, N. 4, p. 777-798, 2007 A. Farina, Y. Sire, E. Valdinoci: Stable solutions of elliptic equations on riemannian manifolds (Preprint) 2008 A. Farina, B. Sciunzi, E. Valdinoci: Bernstein and De Giorgi type problems : new results via a geometric approach Annali della Scuola Normale di Pisa 2008 A. Farina, E. Valdinoci: A pointwise gradient estimate in possibly unbounded domains with nonnegative mean curvature Advances in Mathematics (Accepted Paper) 2009 M. Chermisi, E. Valdinoci: Fibered nonlinearities for $p(x)$-Laplace equations Advances in Calculus of Variations 2009 A. Farina, E. Valdinoci: 1-D symmetry for solutions of semilinear and quasilinear elliptic equations Trans. of the AMS (Accepted Paper) 2009 M. Novaga, E. Valdinoci: Multibump solutions and asymptotic expansions for mesoscopic Allen-Cahn type equations ESAIM Control Optim. Calc. Var. Vol. 15, N. 4, p. 914-933, 2009 M. Chermisi, E. Valdinoci: A symmetry result for a general class of divergence form PDEs in fibered media Nonlinear Analysis Series A: Theory, Methods & Applications Vol. 73, p. 695-703, 2010 A. Farina, E. Valdinoci: Rigidity results for elliptic PDEs with uniform limits : an abstract framework with applications Indiana University Mathematics Journal (Accepted Paper) 2010 A. Farina, E. Valdinoci: Flattening Results for Elliptic PDEs in Unbounded Domains with Applications to Overdetermined Problems Arch. Rational Mech. Anal. Vol. 195, N. 3, p. 1025-1058, 2010 A. Farina, E. Valdinoci: Some results on minimizers and stable solutions of a variational problem Ergodic Theory and Dynamical Systems (Accepted Paper) 2011 A. Farina, E. Valdinoci: A pointwise gradient bound for elliptic equations on compact manifolds with nonnegative Ricci curvature Discrete and Continuous Dynamical System - Series A (Accepted Paper) 2011 A. Farina, Y. Sire, E. Valdinoci: Stable solutions of elliptic equations on riemannian manifolds with euclidean coverings PAMS (Accepted Paper) 2011 M. Novaga, E. Valdinoci: Bump solutions for the mesoscopic Allen-Cahn equation in periodic media Calc. Var. PDE Vol. 40, N. 1-2, p. 37-49, 2011 A. Cesaroni, M. Novaga, E. Valdinoci: Curvature flow in heterogeneous media Interfaces Free Bound. Vol. 13, N. 4, p. 485-505. , 2011 E. Di Nezza, G. Palatucci, E. Valdinoci: Hitchhiker's guide to the fractional Sobolev spaces Bull. Sci. math. Vol. 136, N. 5, p. 521-573, 2012 G. Palatucci, E. Valdinoci: A weighted gradient theory of phase transitions with a possibly singular and degenerate spatial inhomogeneity J. Differential Equations Vol. 252, p. 3381-3402, 2012 B. Barrios, A. Figalli, E. Valdinoci: Bootstrap regularity for integro-differential operators and its application to nonlocal minimal surfaces Ann. Scuola Norm. Sup. Pisa Cl. Sci. (Accepted Paper) 2012 G. Franzina, E. Valdinoci: Geometric analysis of fractional phase transition interfaces Springer INdAM Series p. 18, 2012 A. Farina, E. Valdinoci: On partially and globally overdetermined problems of elliptic type American Journal of Mathematics (Accepted Paper) 2012 A. Pinamonti, E. Valdinoci: A Geometric inequality for stable solutions of semilinear elliptic problems in the Engel group Ann. Acad.Sci.Fenn.Math (Accepted Paper) N. 37, p. 357-373, 2012 A. Farina, E. Valdinoci: Gradient bounds for anisotropic partial differential equations Calc. Var. and PDE (Accepted Paper) 2013 S. Dipierro, A. Figalli, G. Palatucci, E. Valdinoci: Asymptotics of the $s$-perimeter as $s \searrow 0$ Discrete Contin. Dyn. Syst. Vol. 33, N. 7, p. 2777-2790, 2013 A. Farina, L. Mari, E. Valdinoci: Splitting theorems, symmetry results and overdetermined problems for Riemannian manifolds Comm. in PDEs (Accepted Paper) 2013 S. Dipierro, G. Palatucci, E. Valdinoci: Existence and symmetry results for a Schrödinger type problem involving the fractional Laplacian Le Matematiche (Catania) Vol. 68, N. 1, p. 201216, 2013 A. Pinamonti, E. Valdinoci: A Lewy-Stampacchia Estimate for variational inequalities in the Heisenberg group Rend.Istit.Mat.Univ.Trieste (Accepted Paper) Vol. 45, p. 23--45, 2013 G. Palatucci, O. Savin, E. Valdinoci: Local and global minimizers for a variational energy involving a fractional norm Ann. Mat. Pura Appl. Vol. 192, N. 4, p. 673-718, 2013 A. Figalli, E. Valdinoci: Regularity and Bernstein-type results for nonlocal minimal surfaces J. Reine Angew. Math. (Accepted Paper) 2014 A. Cesaroni, M. Novaga, E. Valdinoci: A symmetry result for the Ornstein-Uhlenbeck operator Discrete Contin. Dyn. Syst. A Vol. 34, N. 6, p. 2451-2467, 2014 S. Dipierro, A. Figalli, E. Valdinoci: Strongly nonlocal dislocation dynamics in crystals Comm. Partial Differential Equations (Accepted Paper) 2014 S. Dipierro, G. Palatucci, E. Valdinoci: Dislocation dynamics in crystals: a macroscopic theory in a fractional Laplace setting Comm. Math. Phys. Vol. 3333, N. 2, p. 1061-1105, 2015 A. Di Castro, M. Novaga, B. Ruffini, E. Valdinoci: Nonlocal quantitative isoperimetric inequalities Calc. Var. Partial Differential Equations Vol. 54, N. 3, p. 2421-2464, 2015 A. Farina, E. Valdinoci: 1D SYMMETRY FOR SEMILINEAR PDES FROM THE LIMIT INTERFACE OF THE SOLUTION Comm. in PDE (Accepted Paper ) 2015 A. Farina, E. Valdinoci: REGULARITY AND RIGIDITY THEOREMS FOR A CLASS OF ANISOTROPIC NONLOCAL OPERATORS (Submitted Paper) 2016 S. Dipierro, N. Soave, E. Valdinoci: On fractional elliptic equations in Lipschitz sets and epigraphs: regularity, monotonicity and rigidity results. Mathematische Annalen (Accepted Paper) 2016 E. Cinti, J. Serra, E. Valdinoci: Quantitative flatness results and BV-estimates for stable nonlocal minimal surfaces J. Diff. Geom. (Accepted Paper) 2016 E. Cinti, C. Sinestrari, E. Valdinoci: Neckpinch singularities in Fractional Mean Curvature Flows Proc. Amer. Math. Soc. (Accepted Paper) 2016 C. Geldhauser, E. Valdinoci: Optimizing the fractional power in a model with stochastic PDE constraints (Preprint) 2017 S. Dipierro, A. Pinamonti, E. Valdinoci: Classification of stable solutions for boundary value problems with nonlinear boundary conditions on Riemannian manifolds with nonnegative Ricci curvature Advances in Nonlinear Analysis (Accepted Paper) 2017 F. Maggi, E. Valdinoci: Capillarity problems with nonlocal surface tension energies Comm. PDE (Preprint) 2017 S. Dipierro, M. Novaga, E. Valdinoci: Rigidity of critical points for a nonlocal Ohta-Kawasaki energy Nonlinearity Vol. 30, N. 4, p. 1523-1535, 2017 S. Dipierro, A. Pinamonti, E. Valdinoci: Rigidity results for elliptic boundary value problems: stable solutions for quasilinear equations with Neumann or Robin boundary conditions IMRN (Accepted Paper) 2017 E. Cinti, P. Miraglio, E. Valdinoci: One-dimensional symmetry for the solutions of a three-dimensional water wave problem J. Geom. Anal. (Accepted Paper) 2017 S. Dipierro, F. Maggi, E. Valdinoci: Asymptotic expansions of the contact angle in nonlocal capillarity problems J. Nonlinear Science (Preprint) 2017 A. Massaccesi, E. Valdinoci: Is a nonlocal diffusion strategy convenient for biological populations in competition? Journal of Mathematical Biology Vol. 74, N. 1-2, p. 113-147, 2017 A. Cesaroni, S. Dipierro, M. Novaga, E. Valdinoci: Minimizers for nonlocal perimeters of Minkowski type Calc. Var. Partial Differential Equations Vol. 57, N. 2, p. Art. 64, 40 pages, 2018 E. Cinti, C. Sinestrari, E. Valdinoci: Convex sets evolving by volume preserving fractional mean curvature flows Analysis & PDE (Accepted Paper) 2018 S. Dipierro, A. Pinamonti, E. Valdinoci: Rigidity results in Diffusion Markov Triples J. Funct. Anal. (Accepted Paper) 2018 A. Carbotti, S. Dipierro, E. Valdinoci: Local density of Caputo-stationary functions of any order Complex Variables and Elliptic Equations p. 24, 2018 A. Carbotti, S. Dipierro, E. Valdinoci: Local density of solutions of time and space fractional equations (preprint) 2018 A. Cesaroni, M. Cirant, S. Dipierro, M. Novaga, E. Valdinoci: On stationary fractional Mean Field Games J. Math. Pures Appl. Vol. 122, p. 1-22, 2019 A. Cesaroni, S. Dipierro, M. Novaga, E. Valdinoci: Minimizers of the $p$-oscillation functional Discrete Contin. Dyn. Syst. A Vol. 39, N. 12, p. 6785-6799, 2019 A. Carbotti, S. Dipierro, E. Valdinoci: Local density of Solutions to Fractional Equations (Lecture Notes) Vol. 74, p. 129, 2019 S. Dipierro, M. Novaga, E. Valdinoci: On a Minkowski geometric flow in the plane: Evolution of curves with lack of scale invariance J. London Math. Soc. Vol. 99, N. 1, p. 31-51, 2019 A. Cesaroni, S. Dipierro, M. Novaga, E. Valdinoci: Fattening and nonfattening phenomena for planar nonlocal curvature flows Math. Ann. Vol. 375, N. 1-2, p. 687736, 2019 F. Maggi, E. Valdinoci: Ars Inveniendi Analytica (Announcement) 2020 S. Dipierro, F. Maggi, E. Valdinoci: Minimizing cones for fractional capillarity problems (Preprint) 2020 A. Cesaroni, S. Dipierro, M. Novaga, E. Valdinoci: Heteroclinic connections and Dirichlet problems for a nonlocal functional of oscillation type Annali Mat. Pura e Appl. Vol. 200, N. 5, p. 1999-2041, 2021 S. Dipierro, F. Onoue, E. Valdinoci: (Dis)connectedness of nonlocal minimal surfaces in a cylinder and a stickiness property Proceedings of the AMS (Accepted Paper) p. 13, 2021 S. Dipierro, M. Novaga, E. Valdinoci: Time-fractional Allen-Cahn equations versus powers of the mean curvature Physica D (Accepted Paper) 2024