Research Interests
Calculus of Variations and Partial Differential Equations
- L. Beck, E. Cinti, and C. Seis, Optimal regularity of isoperimetric sets with Holder densities, to appear in Calc. Var. and PDE
- X. Cabré, E. Cinti, and J. Serra, Stable
solutions to the fractional Allen-Cahn equation in the nonlocal perimeter regime, to appear in Amer.
J. Math.
- E. Cinti, R. Ognibene, B. Ruffini,
A quantitative stability inequality for fractional capacities, to appear in Mathematics in Engineering.
- E. Cinti, F. Glaudo, A. Pratelli, X. Ros-Oton, J. Serra,
Sharp quantitative stability for isoperimtric inequalities with homogeneous weights, to appear in Trans. Amer. Math. Soc.
- L. Brasco, E. Cinti, and S. Vita, A quantitative stability estimate for the fractional Faber-Khran inequality, J. Funct. Anal. 279 (2020), no. 3, 108560, 49 pp.
- E. Cinti and F. Colasuonno, A nonlocal supercritical Neumann problem, J. Differential Equations, 268 (2020), no. 5, 2246-2279.
- E. Cinti, C. Sinestrari, and E. Valdinoci, Convex sets evolving by volume preserving Fractional Mean Curvature Flows, Anal. PDE 13 (2020), no. 7, 2149-2171.
- X. Cabré, E. Cinti, and J. Serra, Stable s-minimal cones in R^3 are flat for s\sim 1, J. Reine Angew. Math. (Crelle's Journal), 764 (2020), 157-180.
- E. Cinti, P. Miraglio, and E. Valdinoci, One-dimensional symmetry for the solutions of a three-dimensional water wave problem, J. Geom. Anal. , (2020), no. 2, 1804-1835.
- E. Cinti, J. Serra, and E. Valdinoci, Quantitative flatness results and BV-estimates for stable nonlocal minimal surfaces, J. Differential Geom. 112 (2019), no. 3, 447-504.
- E. Cinti, Flatness results for nonlocal phase transitions, to appear in Contemporary Research in Elliptic PDEs and Related Topics, Springer-INdAM Series (2019) 33, 247-275.
- L. Brasco and E. Cinti, On fractional Hardy inequalities in convex sets, Discrete Contin. Dyn. Syst. 38 (2018), no. 8, 4019-4040.
- E. Cinti, C. Sinestrari, and E. Valdinoci, Neckpinch singularities in Fractional Mean Curvature Flows, Proc. Amer. Math. Soc. 146 (2018), no. 6, 2637-2646.
- E. Cinti, Saddle-shaped solutions for the fractional Allen-Cahn equation, Discrete Contin. Dyn. Syst. Ser. S 11 (2018), no. 3, 441-463.
- E. Cinti, B. Franchi, and M. d. M. Gonzalez, Gamma-convergence of variational functionals with boundary terms in Stein manifolds, Calc. Var. Partial Differential Equations 56 (2017), no. 6, Art. 155, 52 pp.
- E. Cinti and A. Pratelli, Regularity of isoperimetric sets with density in dimension 2, Math. Ann., 368 (2017), no. 1-2, 419-432.
- E. Cinti and A. Pratelli, The ε-ε^β property, the boundedness of
isoperimetric sets in R^N with density, and some applications , J. Reine Angew. Math. (Crelle's Journal), 728 (2017), 65-103.
- E. Cinti and F. Otto, Interpolation inequalities in pattern formation, J. Funct. Anal. 271 (2016), no. 11, 3348-3392.
- E. Cinti, J. Davila, and M. del Pino, Solutions of the fractional Allen-Cahn equations invariant under screw motion, J. Lond. Math. Soc. 94 (2016), no. 1, 295-313.
- E. Cinti and J. Tan, A nonlinear Liouville Theorem for fractional equations in the Heisenberg group, J. Math. Anal. Appl., 433 (2016), no. 1, 434-454.
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E. Cinti and F. Ferrari, Geometric inequalities for fractional Laplace operators and Applications, NoDEA Nonlinear Differential Equations Appl, 22 (2015), no. 6, 1699-1714.
- X. Cabré and E. Cinti, Sharp energy estimates for nonlinear fractional diffusion
equations, Calc. Var & PDE, 49 , (2014), no. 1--2, 233-269.
- E. Cinti, Saddle-shaped solutions of bistable elliptic equations involving the half-Laplacian,
Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 12, (2013), no. 3, 623-664.
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X. Cabré and E. Cinti, Energy estimates and 1D
symmetry for nonlinear equations involving the half-Laplacian,
Discrete and Continuous Dynamical Systems 28, (2010), 1179-1206.
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