Research Papers

51) F. Da Lio, M .Giannocca, Morse Index Stability for the Ginzburg-Landau Approximation, arXiv:2406.07317v2.

50) F. Da Lio, T. Rivière, Conservation Laws for $p$-Harmonic Systems with Antisymmetric Potentials and Applications, arXiv: 2311.04029

49) F. Da Lio, A. Hyder, Blow-up Analysis of Stationary Solutions to a Liouville-Type Equation in 3-D, to be published in Communications in Contemporary Mathematics.

48) F. Da Lio, M .Giannocca, T. Rivière, Morse Index Stability for Critical Points to Conformally invariant Lagrangians, submitted.

47) F. Da Lio, T. Rivière, J. Wettstein, Integrability by compensation for Dirac Equation, Transactions of the American Mathematical Society, Vol. 375, No. 6, June 2022, p. 4477-4511

46) F. Da Lio, K. Mazowiecka, A. Schikorra, A fractional version of Rivière's GL(n)-gauge, Annali di Matematica Pura e Applicata, Volume 201, pages 1817–1853, (2022).

45) F. Da Lio, T. Rivière, J. Wettstein, Bergaman-Bourgain-Brezis type inequality, arXiv:2011.03950, J. Funct. Anal. 281 (2021), no. 9, 33 pp.

44) F. Da Lio, T. Rivière, Critical Chirality in Elliptic Systems, arXiv:1907.10520, Annales de l'Institut Henri Poincaré / Analyse non linéaire, Volume 38,(2021), no 5, 1373-1405.

43) F. Da Lio, T. Rivière, 3-Commutators Revisited, arXiv:1907.10501, Communications in Partial Differential Equations 45 (2020), no. 8, 931–969.

42) F. Da Lio, A. Pigati, Free Boundary Surfaces: A nonlocal Approach, arXiv:1712.04683, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) Vol. XX (2020), 1-53.

41) F. Da Lio, F. Palmurella, T. Rivière, A resolution of the Poisson Problem for elastic plates, arXiv:1807.09373, Archive for Rational Mechanics and Analysis, volume 236, pages 1593–1676 (2020).

40) F. Da Lio, Some remarks on Pohozaev-type identities. Bruno Pini Mathematical Analysis Seminar 2018, 115–136, Bruno Pini Math. Anal. Semin., 9, Univ. Bologna, Alma Mater Stud., Bologna,

39) F. Da Lio, Fractional Harmonic Maps, Recent Developments in Nonlocal Theory Ed. by Palatucci, Giampiero / Kuusi, Tuomo, De Gruyter, 2018.

38) F. Da Lio, F. Palmurella, Remarks on Neumann boundary problems involving Jacobians, Comm. Partial Differential Equations 42 (2017), no. 10, 1497–1509.

37) F. Da Lio, L. Martinazzi, The nonlocal Liouville-type equation in ℝ and conformal immersions of the disk with boundary singularities, arXiv:1607.03525, Calc. Var. Partial Differential Equations 56 (2017), no. 5, Art. 152, 31 pp.

36) F. Da Lio, A. Schikorra, On regularity theory for n/p-harmonic maps into manifolds, arXiv:1709.02329, Nonlinear Anal. 165 (2017), 182–197.

35) F. Da Lio, P. Laurain, T. Rivière, A Pohozaev-type Formula and Quantization of Horizontal Half-Harmonic Maps, arXiv:1607.05504.

34) F. Da Lio, T. Rivière, Horizontal α-Harmonic Maps , arXiv:1604.05461.

33) F. Da Lio, L. Martinazzi, T. Rivière, Blow-up analysis of a nonlocal Liouville-type equation(PDF, 475 KB), arXiv:1503.08701, APDE 8 (2015), 1757-1805.

32) F. Da Lio, Compactness and Bubbles Analysis for Half-Harmonic Maps into Spheres (PDF, 257 KB), arXiv:1210.2653, Annales de l'Institut Henri Poincaré / Analyse non linéaire 32 (2015), 201-224. DOI 10.1016/j.anihpc.2013.11.003.

31) F. Da Lio, Fractional Harmonic Maps into Manifolds in odd dimension $n>1$ (PDF, 251 KB), arXiv:1012.2741v1, Calculus of Variations and PDEs 48, 3-4 (2013), 421-445.

30) F. Da Lio, A. Schikorra, $n/p$-harmonic maps: regularity for the sphere case (PDF, 318 KB), arXiv:1202.1151v1, Adv. Calc. Var. 7 (2014), no. 1, 1–26.

29) F. Da Lio, T. Rivière, Sub-criticality of non-local Schrödinger systems with antisymmetric potentials and applications to half-harmonic maps (PDF, 366 KB), Advances in Mathematics 227 (2011), 1300-1348.

28) F. Da Lio, T. Rivière, 3-Commutators Estimates and the Regularity of 1/2-Harmonic Maps into Spheres (PDF, 362 KB), APDE 4 (2011), 149-190. DOI 10.2140/apde.2011.4.149.

27) F. Da Lio, O. Ley, Uniqueness results for convex Hamilton-Jacobi equations under p>1 growth conditions on data (PDF, 249 KB), Applied Mathematics & Optimization 63 (2011), 309-339.

26) F. Da Lio, Partial Regularity for Stationary Solutions to Liouville-Type Equation in dimension 3 (PDF, 165 KB), Comm. in PDE 33, 10 (2008), 1890-1910.

25) G. Barles, F. Da Lio, P.L. Lions, P. Souganidis, Ergodic problems and periodic homogenization for fully nonlinear equations in half-space type domains with Neumann boundary conditions (PDF, 242 KB), Indiana Univ. Math. J. 57 (2008), 2355-2376.

24) F. Da Lio, Large time behavior of solutions to parabolic equations with Neumann boundary conditions (PDF, 207 KB), J. Math. Anal.Appl. 339 (2008), 384-398.

23) F. Da Lio, N. Forcadel, R. Monneau, Convergence of a nonlocal eikonal equation to anisotropic mean curvature motion. Application to dislocation dynamics (PDF, 287 KB), J. Eur. Math. Soc. 10 (2008), 1061-1104.

22) F. Da Lio, B. Sirakov, Symmetry properties of viscosity solutions to nonlinear uniformly elliptic equations, J. Eur. Math. Soc. 9 (2007), 317-330.

21) A. Cutri, F. Da Lio, Comparison and existence results for non-coercive first order Hamilton-Jacobi equations, ESAIM Control Optim. Calc. Var. 13 (2007), no. 3, 484–502.

21) G. Barles, F. Da Lio, Local $C^{0,\alpha}$ Estimates for Viscosity Solutions to Neumann-type Boundary Value Problems , J. Differential Equations, 225 (2006), 202-241.

20) P. Cardaliaguet, F. Da Lio, N. Forcadel, R. Monneau , Dislocation dynamics : a non-local moving boundary, proceedings du congres FBP 2005, Coimbra, Portugal, International Series of Numerical Mathematics, Vol. 154, Birkhäuser Verlag Basel/Switzerland, 125-135, (2006).

19) F. Da Lio, O. Ley, Uniqueness Results for Second Order Bellman-Isaacs Equations under Quadratic Growth Assumptions and Applications, Siam J. Control. Optim. 45 (2006), 74-106.

18) F. Da Lio, L. Rodino, A Pizzetti-Type Formula for the Heat Operator, Arch. Math. 87 (2006), 261-171.

17) F. Da Lio, A. Montanari, Existence and Uniqueness of Lipschitz Continuous Graphs with Prescribed Levi Curvature, Ann Inst. Henri Poincare, Analyse non lineaire 23 (2006), 1-28.

16) G. Barles, F. Da Lio, On the Boundary Ergodic Problem for Fully Nonlinear Equations in Bounded Domains with General Nonlinear Neumann Boundary Conditions, Ann Inst. Henri Poincare, Analyse non lineaire 22 (2005), 521-541.

15) F. Da Lio, I.Kim, D. Slepcev, Nonlocal Front Propagation Problems in Bounded Domains with Neumann-type Boundary Conditions and Applications, Asymptotic Analysis 37 (2004), 257-292.

14) G. Barles, F. Da Lio, On the Generalized Dirichlet Problem for Viscous Hamilton-Jacobi Equations, J. Math. Pures Appl. 83 (2004), 53-75.

13) F. Da Lio : Remarks on the Strong Maximum Principle for Viscosity Solutions to Fully Nonlinear Parabolic Equations, Communications on Pure and Applied Analysis 3 (2004), 395-415.

12) G. Barles, F. Da Lio, A Geometrical Approach to Front Propagation Problems in Bounded Domains with Neumann-type Boundary Conditions, Interfaces and Free Boundaries 5 (2003), 1-36.

11) G. Barles, F. Da Lio, Remarks on the Dirichlet and State-Constraint Problems for Quasilinear Parabolic Equations, Advances Differential Equations 8 (2003), 897-922.

10) M. Bardi, F. Da Lio, Propagation of maxima and strong maximum principle for viscosity solutions of degenerate elliptic equations. II: Concave operators, Indiana Univ. Math. J. 52 (2003), 607-628.

9) F. Da Lio, Strong Comparison Results for Quasilinear Equations in Annular Domains and Applications, Comm. in PDE 27 (2002), 283-323.

8) F. Da Lio, W.M. McEneaney, Finite Time Horizon Risk Sensitive Control and the Robust Limit under a Quadratic Growth Assumption, Siam J. Control. Optim. 40 (2002), 1628-1661.

7) M. Bardi, F. Da Lio, Propagation of maxima and strong maximum principle for viscosity solutions of degenerate elliptic equations. I: Convex operators, Nonlinear Anal., 44, no.8, Ser A:Theory Methods (2001), 991-1006.

6) F. Da Lio, On the Bellman equation for infinite horizon problems with unbounded cost functional, Appl. Math. Optim. 41 (2000), 171-197.

5) M. Bardi, F. Da Lio, Propagation of maxima and strong maximum principle for viscosity solutions of degenerate elliptic equations. Equadiff99, International conference on differential equations, Berlin 1999. Ed. B.Fiedler, K.Groger and J.Sprekels, Equadiff99 , 2:589-591 , 1999.

4) M. Bardi, F. Da Lio, On the strong maximum principle for fully nonlinear degenerate elliptic equations, Arch.Math. 73 (1999), 276-285.

3) M. Bardi, F. Da Lio, Propagation of Maxima and Strong Maximum Principle for Degenerate Elliptic Equations, Proceeding of the Eighth Tokyo Conference on Nonlinear PDE 1998, 17-28.

2) M. Bardi, S. Bottacin, F. Da Lio, Soluzioni di viscosità di equazioni nonlineari ellittiche degeneri, Giornate dell'Accademia delle Scienze di Bologna, 3-7 Febbraio 1997, Rapporto Interno Università di Padova.

1) M. Bardi, F. Da Lio, On the Bellman equation for some unbounded control problems, Nodea, Nonlinear Differential Equations Appl. 4 (1997), 491-510.