Professore Ordinario MAT05
Dipartimento di Matematica "Ulisse Dini"
degli Studi di Firenze
Viale Morgagni 67/A, 50134 Firenze, Italy
Tel: +39 055 4237491, Fax: +39 055 4222695
Ricerca - Research
My research activity mainly concerns the investigation of geometric (especially convexity) properties of solutions to elliptic and parabolic equations, the study of overdetermined and free-boundary problems, Brunn-Minkowski inequalities for variational functionals, geometric-analytic inequalities and their stability.
Research Program on Nonlinear PDE's - Tohoku University &
Università di Firenze - Firenze, March 3-7,
4th Italian-Japanese Workshop on Geometric Properties for Parabolic and Elliptic PDE's - Palinuro, May 25-29, 2015
BIRS Workshop on Geometric and Analytic Inequalities - Banff,
July 10-15, 2016.
5th Italian-Japanese Workshop on Geometric Properties for Parabolic and Elliptic PDE's - Osaka, May 15-19, 2017
Geometric Aspects of PDEs - Firenze, November 10-11, 2017
UMI-SIMAI-PTM Joint Meeting - Session 20 "Geometric Properties of Solutions of PDEs and Nonlocal Equations"- 17-20 September 2018 -Wroclaw (Poland)
Joint Firenze-Tohoku Research Workshop on Nonlinear PDEs, October 22-23 2018, DiMaI - Firenze
6th Italian-Japanese Workshop on Geometric Properties for Parabolic and Elliptic PDE's - Cortona (Italy), May 20-24, 2019
P. Salani, Convexity of solutions and Brunn-Minkowski inequalities for Hessian equations in R^3, Adv. Math. 229 (2012), 1924-1948.
L. Brasco, R. Magnanini, P. Salani, The location of the hot spot in a grounded convex conductor, Indiana Univ. Math. J. 60 (2011), no. 2, 633–659.
K. Ishige, P. Salani, On a new Kind of convexity for solutions of parabolic problems, Discrete and Continuous Dynamical Systems Series S. (DCDS-S) Vol. 4 n. 4 (2011), 851-864.
Ishige, P. Salani, Parabolic quasi-concavity for solutions to
parabolic problems in convex rings, Math. Nachr. 283 (2010), no.
11, 1526-1548 (rewarded with Editor's Choice).
K. Ishige, P. Salani, Convexity breaking of the free boundary for porous medium equations, Interfaces and Free Boundaries 12 (2010), 75-84.
Brandolini B., Nitsch C., Salani P., Trombetti C., A note on the Serrin problem in the plane, Le Matematiche, Vol. LXIII Fasc. II (2009).
M. Baroni, M. Lombardi, P. Salani, The evolutionary trajectories of countries within the product space of international trade, Oxford Journal (published by the Association for Business & Economics Research) Vol. 8 (2009), 31-47.
Bianchini, P. Salani, Corrigendum to: “Concavity properties for
elliptic free boundary problems” [Nonlinear Anal. 71 (2009) 4461–4470]
Nonlinear Anal., 72 no. 7-8, (2010), page 3551.
C. Bianchini, P. Salani, Concavity properties for elliptic free boundary problems, Nonlinear Anal. 71 no. 10 (2009), 4461-4470.
A. Cianchi, P. Salani, Overdetermined anisotropic elliptic problems, Math. Ann. 345 no. 4 (2009), 859-881.
B. Brandolini, C. Nitsch, P. Salani, C. Trombetti, Stability of radial symmetry for a Monge-Ampère overdetermined problem, Annali Mat. Pura e Appl. (4) 188 no. 3 (2009), 445-453.
C. Bianchini, M. Longinetti, P. Salani, Quasiconcave solutions to elliptic problems in convex rings, Indiana Univ. Math. J. 58 no. 4 (2009), 1565-1589.
B. Brandolini, C. Nitsch, P. Salani, C. Trombetti, On the stability of the Serrin problem, J. Diff. Equations vol. 245, Issue 6 (2008), 1566-1583.
K. Ishige, P. Salani, Is quasi-concavity preserved by heat flow?, Archiv der Mathematik, vol. 90 n.5 (2008), 450-460 (rewarded with Editor's Choice).
B. Brandolini, C. Nitsch, P. Salani, C. Trombetti, Serrin type overdetermined problems: an alternative proof, Arch. Rational Mech. Anal. 190 (2008), 267-280.
M. Longinetti, P. Salani, On the Hessian matrix and Minkowski addition of quasiconvex functions, J. Math. Pures Appl. 88 (2007), 276-292.
P. Cuoghi, P. Salani: Convexity of level sets for solutions to non-linear elliptic problems in convex rings, EJDE vol. 2006 (2006) n. 124, 1-12.
A. Colesanti, P. Cuoghi, P. Salani: Brunn-Minkowski inequalities for two functionals involving the p-Laplace operator, Appl. Anal. vol. 85 n.1-3 (2006), 45-66 (special issue dedicated to the memory of Carlo Pucci).
P. Salani: Starshapedness of level sets of solutions to elliptic PDEs, Appl. Anal. vol. 84 n. 12 (2005), 1185-1197.
P. Salani: A Brunn-Minkowski inequality for the Monge-Ampère eigenvalue, Adv. Math. 194 (2005), 67-86.
A. Colesanti, P. Salani, The Brunn-Minkowski inequality for p-capacity of convex bodies, Math. Ann. 327 (2003), pp. 459-479.
A. Colesanti, P. Salani, Quasi-convex envelope of a function and convexity of level sets of solutions to elliptic equations, Math. Nach. 258 (2003), 3-15
A. Colesanti, E. Francini, P. Salani, Convexity and asymptotic estimates for large solutions of Hessian equations, Differential Integral Equations 13 (2000), n. 10-12, 1459-1472.
P. Salani, Equazioni Hessiane e k-convessità, Boll. U.M.I. (8) 2-A Suppl. (1999), 131-134.
A. Colesanti e P. Salani, Hessian equations in non-smooth domains, Nonlinear Anal. vol. 38 (1999), pp. 803-812.
P. Salani, Boundary blow-up problems for Hessian equations, Manuscripta Mathematica 96 (1998), 281-294.
P. Salani, Equazioni Hessiane e k-convessità, PhD Thesis, Univ. di Firenze (1998) pdf file (Italian)
A. Colesanti e P. Salani, Generalized solutions of Hessian equations, Bull. Australian Math. Soc. vol. 56 (1997), pp. 459-466.
P. Salani, Dispersion of a radioactive tracer in the blood flow, Control and Cybernetics vol. 25 (1996) n 4, pag. 773-788.
S. Baigent, G. Baldini, P. Brand, P. Salani, U. Schulz, The design of a photocopier reflector, Proceedings of the ECMI Modelling Week 1992, Johannes Kepler Universitat, Linz (1992).