PUBLICATIONS



30)
F. Da Lio, T. Riviere  The regularity of solutions to critical non-local Schrödinger systems on the line with antisymmetric potential and applications, preprint 2009.

29) F. Da Lio, T. Riviere,  3-Commutators Estimates and the Regularity of    1/2-Harmonic Maps into  Spheres, accepted in Analysis and PDE.

28) F. Da Lio, O. Ley, Uniqueness results for convex Hamilton-Jacobi equations under p>1 growth conditions on data, preprint 2008.

27) F. Da Lio Partial Regularity for Stationary Solutions to Liouville-Type Equation in dimension 3,  Comm. in PDE, Volume 33, Issue 10 (2008), 1890 - 1910.


26) 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,  Indiana Univ. Math. J. , 57, n.5, (2008), 2355 - 2376.

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

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

23 ) 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

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

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

20)  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) , n.1 , 74-106.

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


18)  A. Cutri`, F. Da Lio, 
Comparison and existence results for non-coercive first order Hamilton-Jacobi equations,     ESAIM: COCV (2007), DOI: 10.1051/cocv: 2007021.

 17) 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, Volume 22  (5)
2005,   521-541.

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

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 (3,4) (2004), 257-292.   

14) 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.

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

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

11)  F. Da Lio,  Strong Comparison Results for Quasilinear Equations in Annular Domains and Applications, Comm. in PDE , 27, n.1 (2002) 283-323.

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

9) 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.

8) 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.

7)  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.

6) 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.

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

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

3)  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 n.5  (2002), 1628-1661.

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

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

 

THESIS

  Degree Thesis :  Equazioni di Bellman per problemi  di controllo ottimo  illimitato.

   PhD Thesis :  Propagation of maxima and uniqueness results for viscosity solutions of  fully  nonlinear  1st and 2nd order equations, Bollettino Unione Matematica Italiana, Aprile 2000.