Alberto Farina


Professeur des Universités

LAMFA
CNRS UMR 7352
Faculté des Sciences
Université de Picardie Jules Verne
33, rue Saint Leu
80039 Amiens CEDEX 1, France

Bureau C  102 bis
Telephone (+33) (0) 3 22 82 76 05
e-mail: Alberto.Farina@u-picardie.fr



Thèmes de recherche développés et mots clés : 

                                        
Curriculum Vitae (Pdf)




Hommage à Enrico Magenes

Hommage à James B. Serrin (AMS)

James B. Serrin (SMAI)





Editeur Associé de Nonlinear Analysis : Theory, Methods & Applications.






[A66] Gradient bound and rigidity results for singular, degenerate, anisotropic partial differential equantions,
to appear in Comm. in Math. Physics, 2013 (with. M. Cozzi, E. Valdinoci).

[A65] Symmetry results for nonlinear elliptic operators with unbounded drift, to appear in Nonlinear Differential
Equations and Applications (NoDEA), 2014 (with M. Novaga, A. Pinamonti).


[A64] Symmetry of components, Liouville-type theorems and classification results for ome nonlinear elliptic systems,
to appear in
DCDS-A (Discrete and Continuous Dynamical Systems - Series A) 2014.

[A63]
A Bernstein-type result for the Minimal Surface Equation, to appear in Annali Scuola Normale Superiore di Pisa, Cl.Sci. (2013).

[A62] Monotonicity and $1$-dimensional symmetry for solutions of an elliptic system arising in Bose-Einstein condensation,
to appear in Archive for Rational Mechanics and Analysis, (2013) (with N. Soave).
DOI: 10.1007/s00205-014-0724-2

[A61] Monotonicity of solutions to quasilinear problems with a first-order term in half-spaces, to appear in
Annales de l’Institut Henri Poincaré́ (C) Non Linear Analysis, 2013 (with L. Montoro, G. Riey, B. Sciunzi).

[A60] Comparison principles, uniqueness and symmetry results of solutions of quasilinear elliptic equations and
inequalities, Nonlinear Analysis: Theory, Methods & Applications 90 (2013) 135-158 (with L. D’Ambrosio, E.
Mitidieri, J. Serrin).

[A59]  Splitting theorems, symmetry results and overdetermined problems for Riemannian manifolds,
Comm. in P.D.E., vol. 38, Issue 10, 2013 (with L. Mari and E. Valdinoci).


[A58]  Monotonicity of solutions of quasilinear degenerate elliptic equations in half-spaces, to appear in Math.
Annalen, 2013 : DOI 10.1007/s00208-013-0919-0 (with L. Montoro and B. Sciunzi).

[A57]  Symmetry and uniqueness of non-negative solutions of some problems in the halfspace, Journal of Math-
ematical Analysis and Applications, 403, (2013),1, 215-233 (with N. Soave).

[A56]  Some symmetry results for entire solutions of an elliptic system arising in phase separation,
DCDS-A (Discrete and Continuous Dynamical Systems - Series A) vol. 34, no. 6, 2014.
 
[A55]  On the classi cation of entire local minimizers of the Ginzburg-Landau equation, Contemporary Mathe-
matics, Vol. 595, AMS, Recent Trends in Nonlinear PDEs II : Stationary Problems, in honor of P. Pucci’s 60th
birthday, 2013, 231-236.


[A54]  Regularity of the extremal solutions for the Liouville system, Geometric Partial Differential Equations
proceedings, Edizioni della Scuola Normale Superiore di Pisa, 2013, 139-144 (with L. Dupaigne et B. Sirakov).


[A53] Gradient bounds for anisotropic partial di fferential equations, to appear in Calculus of Variations and
Partial Di erential Equations, 2012 : DOI 10.1007/s00526-013-0605-9 (with E. Valdinoci).


[A52]  Pointwise estimates and rigidity results for possibly singular and degenerate elliptic PDEs with general
nonlinearities, 
ESAIM : COCV, 19, 2 (2013), 616-627 (with E. Valdinoci).

[A51]  On partially and globally overdetermined problems of elliptic type,  American Journal
of Mathematics, Vol. 135, N. 6, December 2013, 1699-1726 (with E.Valdinoci).

[A50]  Uniqueness of vortexless Ginzburg-Landau type minimizers in two dimensions, Calculus of Variations and
Partial Di erential Equations, 46 (2013), 3-4, 523-544 (with P. Mironescu).

[A49]  Stable solutions of elliptic equations on Riemannian manifolds, Journal of Geometric Analysis, 23, (2013),
3, 1158-1172 (with Y. Sire and E.Valdinoci).

[A48]   Existence and stability of entire solutions to a semilinear fourth order elliptic problem,
to appear
in  J. of Differential Equations, 2011 (with E. Berchio, A. Ferrero and F. Gazzola).

[A47]  Liouville Theorems, to appear in Selected Papers of James Serrin, Contemporary Mathematicians,
3 volumes, (2011). Ed. by P. Pucci, V. Radulescu, H. Weinberger, Birkhauser, Basel.

[A46] Partially and globally overdetermined problems of elliptic type, Advances in Nonlinear Analysis. Volume
1, Issue 1, 2012, 27-45 (with E. Valdinoci).

[A45] A pointwise gradient estimate for solutions of singular and degenerate PDEs in possibly unbounded do-
mains with nonnegative mean curvature, Communications on Pure and Applied Analysis, Vol. 11, 5, 2012,
1983-2003 (with D. Castellaneta and E. Valdinoci).

[A44] Stable solutions of elliptic equations on Riemannian manifolds with Euclidean coverings,  Proc. Amer. Math.
Soc., Vol.140, 3, 2012, 927-930 (with Y. Sire and E.Valdinoci).

[A43] Some results on minimizers and stable solutions of a variational problem, Ergod. Th. and Dynam. Sys.
(2012), 32, 1302-1312 (with E. Valdinoci).

[A42] Monotonicity and one-dimensional symmetry for solutions of $ -\Delta_p(u) = f(u) $ in half-spaces, Calculus of
Variations and Partial Di erential Equations: Vol.43, Issue 1 (2012), 123-145 (with L. Montoro and B. Sciunzi).

[A41] Partial regularity of finite Morse index solutions to the Lane-Emden equation,
Journal of Functional
Analysis, 261, (2011) 218-232 (with J. Davila and L. Dupaigne).

[A40] Entire solutions of completely coercive quasilinear elliptic equations,
J. of Differential Equations, 250
(2011), 4367-4408 (with  J. Serrin).

[A39] Rigidity results for elliptic PDEs with uniform limits: an abstract framework with applications, Indiana
University Mathematics Journal, Vol. 60,1,2011 (with E. Valdinoci).

[A38] A pointwise gradient bound for elliptic equations on compact manifolds with nonnegative Ricci curvature,
DCDS-A (Discrete and Continuous Dynamical System - Series A), Vol. 30, No. 4, 2011 (with E.
Valdinoci).

[A37] Entire solutions of completely coercive quasilinear elliptic equations, II,
J. of Differential Equations, 250 (2011) 4409-4436 (with  J. Serrin).

[A36] A pointwise gradient estimate in possibly unbounded domains with nonnegative mean curvature,
Advances in Mathematics 225 (2010), 2808 - 2827 (with E. Valdinoci).

[A35] Flattening results for elliptic PDEs in unbounded domains with applications to overdetermined problems,
Archive for Rational Mechanics and Analysis, 195 (2010), 1025 - 1058 (with E. Valdinoci).

[A34] Stable solutions of  $- \Delta u = f(u)$ in IR^N,
JEMS -Journal of the European Mathematical Society, Volume
12, Issue 4, 2010, pp. 855 - 882 (with L. Dupaigne).

[A33] 1D symmetry for solutions of semilinear and quasilinear elliptic equations,
Trans. of the AMS, Volume
363, Number 2, February 2011, Pages 579 - 609 (with E. Valdinoci).

[A32] On a Poincaré type formula for solutions of singular and degenerate elliptic equations,
Manuscripta
Math.,Vol.132, Issue 3 (2010), 335-342 (with B. Sciunzi and E. Valdinoci).

[A31] Overdetermined problems in unbounded domains with Lipschitz singularities,
Rev. Matemtica Iberoamericana
26 (2010), no. 3, 965 - 974 (with E. Valdinoci).

[A30] Liouville Theorems for stable solutions of semilinear elliptic equations with convex nonlinearities,
Nonlinear Analysis: Theory, Methods & Applications Vol.70, Issue 8, 15 April 2009, 2882-2888 (with L. Dupaigne).

[A29] Bernstein and De Giorgi type problems: new results via a geometric approach,
Annali Scuola Normale
Superiore di Pisa, Cl.Sci.(5),7,2008 (with B. Sciunzi and E.Valdinoci).

[A28] On the classification of solutions of $ −\Delta u = e^u $  on IR^N : stability outside a compact set and applications,
Proc. Amer. Math. Soc. 137 (2009),1333-1338 (with E.N. Dancer).

[A27] Liouville results for m-Laplace equations of Lane-Emden-Fowler type,
Annales de l’Institut Henri
Poincaré (C) Non Linear Analysis, Vol.26, Issue 4, July-August 2009, 1099-1119
(with L. Damascelli, B. Sciunzi and E. Valdinoci).

[A26] Some Liouville-type theorems for elliptic equations and their consequencesBoletin SEMA, n.45, 2008.

[A25] Liouville-type Theorems for elliptic problems,
Ch. 2, pp.61-116, in
Handbook of Differential Equations: Stationary Partial Differential Equations. Vol. 4, 2007,
Ed. by M.Chipot, Elsevier B.V.

[A24] The state of the art for a conjecture of De Giorgi and related problems, Ch. in the book : Recent
Progress on Reaction-Diffusion Systems and Viscosity Solutions, Mars 2009. Edited by H.Ishii, W.-Y.Lin
and Y.Du, World Scientific.

[A23] Geometry of quasiminimal phase transitions,
Calculus of Variations and Partial Differential Equations,
Volume 33, Number 1, septembre 2008 (with E. Valdinoci).

[A22] Remarks on an overdetermined boundary value problem,
Calculus of Variations and Partial Differential
Equations, Volume 31, Number 3, mars 2008 (with B. Kawohl).

[A21] Stable solutions of $ −\Delta u = e^u $  on IR^N ,
Comptes Rendus Mathmatique,Volume 345, Issue 2, 15 July
2007, Pages 63-66.

[A20] A Liouville property for Ginzburg-Landau systems,
Analysis and Applications, Volume 5, Issue 3 (July
2007), 285-290.

[A19] On the classification of solutions of the Lane-Emden equation on unbounded domains of IR^N ,
 Journal de Mathématiques Pures et Appliquées,Volume 87, Issue 5, May 2007, 537-561.

[A18] Liouville-type results for solutions of  $ −\Delta u = |u|^{p1}u $ on unbounded domains of IR^N,
Comptes Rendus de l’Académie des Sciences de Paris, 41 (2005), no. 7, 415-418.

[A17] Sym´etrie pour les solutions d’´equations elliptiques : une approche g´eom´etrique,
dans Habilitation à
diriger des recherches, Université Paris VI, 2002.

[A16] Two results on entire solutions of Ginzburg-Landau system in higher dimensions,
Journal of Functional
Analysis, Vol. 214, Issue 2, p. 386-395. (2004).

[A15] From Ginzburg-Landau to Gross-Pitaevskii, Monatshefte fur Mathematik 139, (2003),265-269.

[A14] Rigidity and one-dimensional symmetry for semilinear elliptic equations in the whole of IR^N and in half spaces,
Advances in Mathematical Sciences and Applications, v.13, no. 1, (2003),65-82.

[A13] One-dimensional symmetry for solutions of quasilinear equations in IR^2,
Bollettino UMI, (8), 6-B,
(2003), pp. 685-692.

[A12] Monotonicity and one-dimensional symmetry for the solutions of $ −\Delta u + f(u) = 0 $ in IR^N with possibly discontinuous nonlinearity,
Advances in Mathematical Sciences and Applications, Vol. 11, no. 2 (2001),
pp.811-834.

[A11] Qualitative study of radial solutions of the Ginzburg-Landau systems in IR^N, ($N \ge  3$),
Applied Math.
Letters, Vol. 13, 7, 2000, pp.59-64 (with M.Guedda).

[A10] Propriétés de monotonie et de symétrie unidimensionnelle pour les solutions de $ −\Delta u + f(u) = 0 $ avec des fonctions
f éventuellement discontinues
, Comptes Rendus de l’Académie des Sciences de Paris, t.330, Série I, 2000, pp. 973-978.

[A9] Ginzburg-Landau type elliptic systems in IR^2,
Gakuto International Series Mathematical Sciences and
Applic., Vol. 13, Free Boundary Problems : Theory and Applications I, 2000, 54-63.

[A8] Symmetry for solutions of semilinear elliptic equations in IR^N and related conjectures,
Rendiconti Accademia
Nazionale dei Lincei - Sez. Matematica e Applic., serie IX, Vol. X, 1999 -Fasc. 4, pp.255-265.

[A7] Symmetry for solutions of semilinear elliptic equations in IR^N and related conjectures,
Ricerche di
Matematica: special issue in Memory of E. De Giorgi, Vol. XLVIII, Suppl.1999, pp. 129-154.

[A6] Some remarks on a conjecture of De Giorgi,
Calculus of Variations and Partial Differential Equations,
8, 1999, 3, pp. 233-245.

[A5] Finite-Energy solutions, quantization effects and Liouville-type results for a variant of the Ginzburg-Landau systems in IR^K,
Differential and Integral Equations, Vol.11, 6, November 1998, pp. 875-893.

[A4] Sur les solutions radiales de l'équation $ −\Delta u = u(1 − |u|^2) dans IR^N, ($N \ge  3$),
Comptes Rendus de l’Académie des Sciences de Paris t.325, Série I, 1997, pp.601-604 (with V. Akopian).

[A3] Finite-Energy solutions, quantization effects and Liouville-type results for a variant of the Ginzburg-Landau systems in IR^K,
Comptes Rendus de l’Académie des Sciences de Paris, t.325, Série I, 1997, pp.487-491.

[A2] BV and Nikolskii spaces and applications to the Stefan problem,
Rendiconti Accademia Nazionale dei
Lincei - Sez. Matematica e Applic. serie IX, Vol. VI, 1995 - Fasc. 3, pp.143-154.

[A1] Sulle condizioni puntuali perché una funzione infinitamente derivabile sia analitica o polinomiale,
Rendiconti
Istituto Lombardo, Scienze Matem. e Applic. Vol. 127 (1993) - Fasc. 1, pp.41-52.



                                                                            Ouvrages Scientifiques



[OS1]  Liouville-type Theorems for elliptic problems,
Ch.2, pp. 61-116, in Handbook of
Differential Equations : Stationary Partial Differential Equations. Vol. 4, 2007, Edited by M.Chipot, Elsevier B.V.

[OS2]
  The state of the art for a conjecture of De Giorgi and related problems,
Ch. in the book : Recent
Progress on Reaction-Diffusion Systems and Viscosity Solutions, Mars 2009. Edited by H.Ishii, W.-Y.Lin and Y.Du, World Scientific.

[OS3] Editor ( with J-C. Saut) of : Proceedings of the Summer School ” Gross-Pitaevskii equations for superfluids and Bose-Einstein condensates ”,
Vienna (Austria), Sept. 2006. Contemporary Mathematics - AMS - Vol.473, 2008.

[OS4] Editor (with E. Valdinoci) of : Symmetry for elliptic PDEs: 30 years after a conjecture of De Giorgi and related problems,
Proceedings of INdAM School, Mai 2009, Rome (Italie). Contemporary Mathematics - AMS, Vol. 528, 2010.



                                                           Activité éditoriale


* Editeur Associé de Nonlinear Analysis : Theory, Methods & Applications.

Editor ( with J-C. Saut) of : Proceedings of the Summer School ” Gross-Pitaevskii equations for superfluids and Bose-Einstein condensates ”,
Vienna (Austria), Sept. 2006. Contemporary Mathematics - AMS - Vol.473, 2008.

* Editor (with E. Valdinoci) of : Symmetry for elliptic PDEs: 30 years after a conjecture of De Giorgi and related problems,
Proceedings of INdAM School, Mai 2009, Rome (Italie). Contemporary Mathematics - AMS, Vol. 528, 2010.



                                                             Travaux