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Bureau C 102 bis
Telephone (+33) (0) 3 22 82 76 05
e-mail:
Alberto.Farina@u-picardie.fr
Publications
[A51] On
partially and globally overdetermined problems of elliptic
type, to appear in American Journal of
Mathematics, 2012 : http://www.math.jhu.edu/ ajm/acc-12.htm
(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).
[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,
to appear in Proc. Amer. Math. Soc., 2011 (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 consequences, Boletin 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|^{p−1}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.
* 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.
1) Propriétés qualitatives de
solutions d'équations et systèmes d'équations non-linéaires,
Habilitation à diriger des recherches, Paris VI, 13-12-2002.
2) Quelques résultats sur les systèmes de Ginzburg-Landau et leurs généralisations, Thèse de doctorat, Ecole polytechnique, 18-12-1997.
3) Spazi BV e di Nikolskii e applicazioni al
problema di Stefan, Laurea in
matematica, Università di Pavia (Italie) , 25- 5-1994.
Liens
Séminaire d'analyse appliquée A3
Groupe
de travail analyse appliquée A 3
Dipartimento di Matematica dell'Università di Pavia
Centre de Mathématiques de l'Ecole polytechnique
Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie - Paris VI