Paolo SALANI

Ruolo attuale:: Professore Ordinario
SSD:: MATH-03/A - Analisi matematica
Afferenza organizzativa:: Dipartimento di Matematica e Informatica 'Ulisse Dini'

Recapiti

	0552751418
	paolo.salani(AT)unifi.it

Ulteriori Recapiti

	Viale Morgagni 67/A - Stanza 019
	0552751418
	paolo.salani(at)unifi.it
	www.math.unifi.it/users/salani

Paolo SALANI

Orario di ricevimento (aggiornato al 17/04/2014)

Ogni giorno su appuntamento. Contattare il docente via email.

Paolo SALANI

Curriculum

Nato a Firenze il 3/12/1968.

Laureato in Matematica il 16/7/1993. Dottorato in Matematica conseguito il 10/7/1998.

Analista-programmatore presso l'Azienda Ospedaliera "Meyer" di Firenze dal 20/1/1998 al 31/8/2000.

Ricercatore in Analisi Matematica presso l'Università di Firenze dal 1/9/2000 al 22/11/2011.

Professore Associato in Analisi Matematica presso l'Università di Firenze dal 23/12/2011 al 30/10/2017.

Professore Ordinario di Analisi Matematica presso l'Università di Firenze dal 1/11/2017.

Coordinatore del Dottorato in Matematica, Informatica, Statistica dell'Università di Firenze (in consorzio con Università di Perugia e INdAM) dal XXXIII al XXXVI ciclo.

Direttore del DiMaI (Dip. Matematica e Informatica) "U. Dini" dal 1/11/2020 al 27/2/2023.

Direttore della Fondazione CIME (Centro Internazional Matematico Estivo) "Roberto Conti" dal 25/1/2023. In precedenza, Segretario Scientifico e Tesoriere della Fondazione CIME dal 1/1/2015 al 25/1/2023.

Paolo SALANI

Interessi La mia attività di ricerca riguarda principalmente lo studio delle proprietà geometriche (specialmente convessità e simmetria) di soluzioni di equazioni alle derivate parziali di tipo ellittico e parabolico. Mi occupo anche di problemi sovradeterminati, problemi a frontiera libera e di disuguaglianze di tipo Brunn-Minkowski per funzionali variazionali e disuguaglianze di tipo isoperimetrico.

Paolo SALANI

Pubblicazioni

Legenda

Contributo su rivista |

Articolo su libro |

Libro |

Contributo in atti di convegno (proceeding) |

Brevetto |

Curatela | Altro

Altro |

Tesi di Dottorato

Ishige K.; Salani P.; Takatsu A. (2024). CHARACTERIZATION OF F-CONCAVITY PRESERVED BY THE DIRICHLET HEAT FLOW. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, vol. 377, pp. 5705-5748, ISSN:0002-9947 DOI Accesso ONLINE all'editore

Cianchi A.; Salani P. (2023). Wulff shape symmetry of solutions to overdetermined problems for Finsler Monge-Ampère equations. JOURNAL OF FUNCTIONAL ANALYSIS, vol. 285, pp. 0-0, ISSN:0022-1236 DOI

Ishige K.; Salani P.; Takatsu A. (2023). Hierarchy of deformations in concavity. INFORMATION GEOMETRY, vol. 7, pp. 251-269, ISSN:2511-2481 DOI Accesso ONLINE all'editore

Jarohs S.; Kulczycki T.; Salani P. (2022). On the Bernoulli free boundary problems for the half Laplacian and for the spectral half Laplacian. NONLINEAR ANALYSIS, vol. 222, pp. 0-0, ISSN:0362-546X DOI Accesso ONLINE all'editore

Ishige K.; Salani P.; Takatsu A. (2022). Power concavity for elliptic and parabolic boundary value problems on rotationally symmetric domains. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, vol. 24, pp. 0-0, ISSN:0219-1997 DOI Accesso ONLINE all'editore

Ishige K.; Salani P.; Takatsu A. (2022). New characterizations of log-concavity via Dirichlet heat flow. ANNALI DI MATEMATICA PURA ED APPLICATA, vol. 201, pp. 1531-1552, ISSN:0373-3114 DOI Accesso ONLINE all'editore

Ferone V.; Kawakami T.; Salani P.; Takahashi F. (2021). Geometric Properties for Parabolic and Elliptic PDEs. Springer-Verlag Italia s.r.l., pp. 1-305, 978-1-4244-0577-0. Accesso ONLINE all'editore

Ishige, K; Nakagawa, K; Salani, P (2020). Spatial concavity of solutions to parabolic systems. ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE, vol. 20, pp. 291-313, ISSN:0391-173X DOI Accesso ONLINE all'editore

Ishige, Kazuhiro; Salani, Paolo; Takatsu, Asuka (2020). To logconcavity and beyond. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, vol. 22, pp. 0-0, ISSN:0219-1997 DOI Accesso ONLINE all'editore

Ishige K.; Liu Q.; Salani P. (2020). Parabolic Minkowski convolutions and concavity properties of viscosity solutions to fully nonlinear equations. JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES, vol. 141, pp. 342-370, ISSN:0021-7824 DOI Accesso ONLINE all'editore

Campi, Stefano; Gronchi, Paolo; Salani, Paolo (2019). A proof of a Loomis–Whitney type inequality via optimal transport. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol. 471, pp. 489-495, ISSN:0022-247X DOI

Federica Dragoni, Nicola Garofalo, Paolo Salani (2019). Starshapedeness for fully non-linear equations in Carnot groups. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY, vol. 99, pp. 901-918, ISSN:0024-6107 DOI Accesso ONLINE all'editore

Chuanqiang, Chen; Xi-Nan, Ma; Paolo, Salani (2019). On space-time quasiconcave solutions of the heat equation. MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, vol. 259, pp. 0-0, ISSN:0065-9266 DOI Accesso ONLINE all'editore

Rossi, Andrea*; Salani, Paolo (2019). Stability for a strengthened Borell–Brascamp–Lieb inequality. APPLICABLE ANALYSIS, vol. 98, pp. 1773-1784, ISSN:0003-6811 DOI Accesso ONLINE all'editore

Jarohs, Sven; Kulczycki, Tadeusz; Salani, Paolo (2019). Starshapedness of the superlevel sets of solutions to equations involving the fractional Laplacian in starshaped rings. MATHEMATISCHE NACHRICHTEN, vol. 292, pp. 1008-1021, ISSN:0025-584X DOI Accesso ONLINE all'editore

Henrot, Antoine; Nitsch, Carlo; Salani, Paolo; Trombetti, Cristina* (2018). Optimal Concavity of the Torsion Function. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, vol. 178, pp. 26-35, ISSN:0022-3239 DOI Accesso ONLINE all'editore

Chiara Bianchini, Giulio Ciraolo, Paolo Salani (2018). Some overdetermined problems related to the anisotropic capacity. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol. 465, pp. 211-219, ISSN:0022-247X DOI

Daria, Ghilli; Paolo, Salani (2017). Quantitative Borell-Brascamp-Lieb inequalities for power concave functions. JOURNAL OF CONVEX ANALYSIS, vol. 24, pp. 857-888, ISSN:0944-6532 Accesso ONLINE all'editore

Andrea, Rossi; Paolo, Salani (2017). Stability for Borell-Brascamp-Lieb inequalities. In: Bo'az Klartag, Emanuel Milman (Editors). Geometric Aspects of Functional Analysis, pp. 339-363, Heidelberg Germania: Springer Verlag. DOI Accesso ONLINE all'editore

Salani, P (2017). OPTIMAL CONCAVITY FOR NEWTONIAN POTENTIALS. BRUNO PINI MATHEMATICAL ANALYSIS SEMINAR, vol. 1, pp. 26-42, ISSN:2240-2829 DOI Accesso ONLINE all'editore

Chiara Bianchini; Giulio Ciraolo; Paolo Salani; (2016). An overdetermined problem for the anisotropic capacity. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, vol. 55, pp. 1-24, ISSN:0944-2669 DOI Accesso ONLINE all'editore

Talenti, Giorgio; Colesanti, Andrea; Salani, Paolo (2016). Un'introduzione al Calcolo della Variazioni: teoria ed esercizi. Bologna: Unione Matematica Italiana, ISBN:978-8896336205

Ishige, Kazuhiro; Salani, Paolo (2016). Parabolic Minkowski convolutions of solutions to parabolic boundary value problems. ADVANCES IN MATHEMATICS, vol. 287, pp. 640-673, ISSN:0001-8708 DOI Accesso ONLINE all'editore

Gazzola, Filippo; Nitsch, Carlo; Ishige, Kazuhiro; Salani, Paolo (2016). Italian-Japanese workshop on Geometric Properties for Parabolic and Elliptic PDE’s, GPPEPDEs 2015. In: Filippo Gazzola, Carlo Nitsch, Kazuhiro Ishige, Paolo Salani. Springer Proceedings in Mathematics and Statistics, pp. 1-288 Springer New York LLC, ISBN:9783319415369. DOI Accesso ONLINE all'editore

Ishige, Kazuhiro; Nakagawa, Kazushige; Salani, Paolo (2016). Power concavity in weakly coupled elliptic and parabolic systems. NONLINEAR ANALYSIS, vol. 131, pp. 81-97, ISSN:0362-546X DOI Accesso ONLINE all'editore

Paolo Salani (2015). Combination and mean width rearrangements of solutions to elliptic equations in convex sets. ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE, vol. 32, pp. 763-783, ISSN:0294-1449 DOI Accesso ONLINE all'editore

Paolo Salani (2015). A characterization of balls through optimal concavity for potential functions. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, vol. 143, pp. 173-183, ISSN:0002-9939 DOI Accesso ONLINE all'editore

Andrea Colesanti; Kaj Nystrom; Paolo Salani; Jie Xiao; Deane Yang; Gaoyong Zhang (2015). THE HADAMARD VARIATIONAL FORMULA AND THE MINKOWSKI PROBLEM FOR p-CAPACITY. ADVANCES IN MATHEMATICS, vol. 285, pp. 1511-1588, ISSN:0001-8708 DOI Accesso ONLINE all'editore

Paolo Salani; Kazuhiro Ishige (2014). Parabolic power concavity and parabolic boundary value problems. MATHEMATISCHE ANNALEN, vol. 358, pp. 1091-1117, ISSN:0025-5831 DOI

Chiara Bianchini; Antoine Henrot; Paolo Salani (2014). An overdetermined problem with non-constant boundary condition. INTERFACES AND FREE BOUNDARIES, vol. 16, pp. 215-241, ISSN:1463-9963 DOI

D. Ghilli; P. Salani (2014). Stability of isoperimetric type inequalities for some Monge–Ampère functionals. ANNALI DI MATEMATICA PURA ED APPLICATA, vol. 193, pp. 643-661, ISSN:0373-3114 DOI Accesso ONLINE all'editore

Ishige, Kazuhiro; Salani, Paolo (2014). A note on parabolic power concavity. KODAI MATHEMATICAL JOURNAL, vol. 37, pp. 668-679, ISSN:0386-5991 DOI Accesso ONLINE all'editore

Chiara Bianchini; Paolo Salani (2013). A note on an overdetermined problem with non-constant boundary condition. SUURI KAISEKI KENKYUUJO KOUKYUUROKU, vol. 1850, pp. 79-89, ISSN:1880-2818 Accesso ONLINE all'editore

M. Bianchini; P. Salani (2013). Power concavity for solutions of nonlinear elliptic problems in convex domains. In: Magnanini, Rolando; Sakaguchi, Shigeru; Alvino, Angelo (Eds.). Geometric Properties for Parabolic and Elliptic PDE's, pp. 35-48, Berlino: Springer Inernational Publishing, ISBN:9788847028418. DOI Accesso ONLINE all'editore

P. Salani (2012). Convexity of solutions and Brunn–Minkowski inequalities for Hessian equations in R^3. ADVANCES IN MATHEMATICS, vol. 229, pp. 1924-1948, ISSN:0001-8708 DOI Accesso ONLINE all'editore

K. Ishige; P. Salani (2011). On a new kind of convexity for solutions of parabolic problems. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S, vol. vol. 4, pp. 851-864, ISSN:1937-1632 DOI

L. Brasco; R. Magnanini; P. Salani (2011). The location of the hot spot in a grounded convex conductor. INDIANA UNIVERSITY MATHEMATICS JOURNAL, vol. 60, pp. 633-660, ISSN:0022-2518 DOI

K. Ishiige; P. Salani (2010). Parabolic quasi-concavity for solutions to parabolic problems in convex rings. MATHEMATISCHE NACHRICHTEN, vol. 283 issue 11, pp. 1526-1548, ISSN:0025-584X DOI Accesso ONLINE all'editore

C. Bianchini; P. Salani (2010). Corrigendum to: "Concavity properties for elliptic free boundary problems'' [Nonlinear Anal. 71 (2009) 4461–4470]. NONLINEAR ANALYSIS, vol. Volume 72, Issues 7–8, pp. 3551-3551, ISSN:0362-546X DOI Accesso ONLINE all'editore

K. Ishige; P. Salani (2010). Convexity breaking of the free boundary for porous medium equations. INTERFACES AND FREE BOUNDARIES, vol. 12 issue 1, pp. 75-84, ISSN:1463-9963 DOI

C. BIANCHINI; M. LONGINETTI; P. SALANI (2009). Quasiconcave solutions to elliptic problems in convex rings. INDIANA UNIVERSITY MATHEMATICS JOURNAL, vol. 58, pp. 1565-1589, ISSN:0022-2518 DOI Accesso ONLINE all'editore

B. Brandolini; C. Nitsch; P. Salani; C. Trombetti (2009). Stability of radial symmetry for a Monge-Ampère overdetermined problem. ANNALI DI MATEMATICA PURA ED APPLICATA, vol. 188 n.3, pp. 445-453, ISSN:0373-3114 DOI Accesso ONLINE all'editore

C. Bianchini; P. Salani (2009). Concavity properties for elliptic free boundary problems. NONLINEAR ANALYSIS, vol. 71, pp. 4461-4470, ISSN:0362-546X DOI

M. Lombardi; P. Salani; M. Baroni (2009). The evolutionary trajectories of countries within the product space of international trade. OXFORD JOURNAL, vol. 8 n.1, pp. 31-47, ISSN:1551-4498

A. Cianchi; P. Salani (2009). Overdetermined anisotropic elliptic problems. MATHEMATISCHE ANNALEN, vol. 345, pp. 859-881, ISSN:0025-5831

B. Brandolini; C. Nitsch; P. Salani; C. Trombetti (2008). On the stability of the Serrin problem. JOURNAL OF DIFFERENTIAL EQUATIONS, vol. 245 n.6, pp. 1566-1583, ISSN:0022-0396 DOI

B. BRANDOLINI; C. NITSCH; P. SALANI; C. TROMBETTI (2008). Serrin type overdetermined problems: an alternative proof. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, vol. 190 n. 2, pp. 267-280, ISSN:0003-9527 DOI

K. ISHIGE; P. SALANI (2008). Is quasi-concavity preserved by heat flow?. ARCHIV DER MATHEMATIK, vol. vol. 90 n.5, pp. 450-460, ISSN:0003-889X, Birkhaeuser Verlag AG:Viaduktstrasse 42-44, CH 4051 Basel Switzerland:011 41 61 2050707, EMAIL: subscriptions@birkhauser.ch, INTERNET: http://www.birkhauser.ch, Fax: 011 41 61 2050792: Accesso ONLINE all'editore

B. Brandolini; C. Nitsch; P. Salani; C. Trombetti (2008). A note on the Serrin Problem in the plane. LE MATEMATICHE, vol. 63, pp. 83-92, ISSN:0373-3505

M. LONGINETTI; P. SALANI (2007). On the Hessian matrix and Minkowski addition of quasiconvex functions. JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES, vol. 88, pp. 276-292, ISSN:0021-7824 DOI

A. COLESANTI; P. CUOGHI; P. SALANI (2006). Brunn-Minkowski inequality for two functionals involving the p-Laplace operator. APPLICABLE ANALYSIS, vol. 85 (1-3), pp. 45-66, ISSN:0003-6811

P. CUOGHI; P. SALANI (2006). Convexity of level sets for solutions to non-linear elliptic problems in convex rings. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, vol. 2006, pp. 1-12, ISSN:1072-6691 Accesso ONLINE all'editore

P. SALANI (2005). A Brunn-Minkowski inequality for the Monge-Ampère eigenvalue. ADVANCES IN MATHEMATICS, vol. 194, pp. 67-86, ISSN:0001-8708 DOI

P. SALANI (2005). Starshapdness of level sets of solutions to elliptic equations. APPLICABLE ANALYSIS, vol. 84 (12), pp. 1185-1197, ISSN:0003-6811

A. COLESANTI; P. SALANI (2003). Quasi-concave envelope of a function and convexity of level sets of solutions to elliptic equations. MATHEMATISCHE NACHRICHTEN, vol. 258, pp. 3-15, ISSN:0025-584X

A. COLESANTI; P. SALANI (2003). THE BRUNN-MINKOWSKI INEQUALITYY FOR P-CAPACITY OF CONVEX BODIES. MATHEMATISCHE ANNALEN, vol. 327, pp. 459-479, ISSN:0025-5831

A. COLESANTI; E. FRANCINI; P. SALANI (2000). Convexity and asymptotic estimates for large solutions of Hessian equations. DIFFERENTIAL AND INTEGRAL EQUATIONS, vol. 13 N. 10-12, pp. 1459-1472, ISSN:0893-4983

Salani P. (1999). Equazioni hessiane e k-convessità. BOLLETTINO DELL'UNIONE MATEMATICA ITALIANA. A, vol. 2, pp. 131-134, ISSN:0392-4033

A. COLESANTI; P. SALANI (1999). Hessian equations in non smooth domains. NONLINEAR ANALYSIS, vol. 38, pp. 803-812, ISSN:0362-546X DOI Accesso ONLINE all'editore

P. Salani (1998). Boundary blow-up problems for Hessian equations. MANUSCRIPTA MATHEMATICA, vol. 96, pp. 281-294, ISSN:0025-2611

P. Salani (1998). Equazioni Hessiane e k-convessità. (Tutor: S. Campi)

A. Colesanti; P. Salani (1997). Generalized solutions of Hessian equations. BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, vol. 56 n. 3, pp. 459-466, ISSN:0004-9727

Paolo SALANI

Curriculum

Born in Florence (Italy), 3/12/1968. Degree in Mathematics, 16/7/1993. PhD in Mathematics, 10/7/1998.

From 20/1/1998 to 31/8/2000 I worked as systems analyst and analyst-programmer at the Azienda Ospedaliera "Meyer" in Florence.

I am Full Professor at the Department of Mathematics and Informatics "U. Dini" of the University of Florence since 1/11/2017 (formerly Asscoaiet Professor since 23/12/2011 and before Researcher since 1/9/2000).

Dean of the Department of Mathematics and Computer Science from 1/11/2020 to 27/2/2023.

Director of CIME Foundation "R. Conti" since 25/1/2023. Previously, Scientific Secretary of CIME since 2015.

Coordinator of the PhD School in Mathematics, Computer Science, Statistics of Università di Firenze form XXXIII to XXXVI cycle.

Paolo SALANI

Interest 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.