Paolo SALANI

Ruolo attuale:: Professore ordinario
SSD:: MAT/05 - Analisi matematica
Afferenza organizzativa:: Dipartimento di Matematica e Informatica 'Ulisse Dini'

Recapiti

	055 2751463
	paolo.salani(AT)unifi.it salani(AT)math.unifi.it

Ulteriori Recapiti

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, voto 110/110 e lode.

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 (posizione attuale) presso l'Università di Firenze dal 23/12/2011.

Abilitato al ruolo di Professore Ordinario in Analisi Matematica (in data 310/12/2013).

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, 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; 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 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

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

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

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

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

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

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

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

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

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 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

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

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

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

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

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

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

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

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

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

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. 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

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; 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. 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 (2009). Concavity properties for elliptic free boundary problems. NONLINEAR ANALYSIS, vol. 71 n. 10, pp. 4461-4470, ISSN:0362-546X

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

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

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

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). 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). A note on the Serrin Problem in the plane. LE MATEMATICHE, vol. 63, pp. 83-92, ISSN:0373-3505

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

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

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

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. 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

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

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

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

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

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

Insegnamenti relativi all'Anno Accademico

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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 Associate Professor at the Department of Mathematics and Informatics "U. Dini" of the University of Florence since 23/12/2011 (formerly Researcher since 1/9/2000).

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.

Paolo SALANI

Paolo SALANI

Paolo SALANI

Paolo SALANI

Paolo SALANI

Paolo SALANI

Insegnamenti relativi all'Anno Accademico 2020-2021 2019-2020 2018-2019 2017-2018 2016-2017 2015-2016 2014-2015 2013-2014 2012-2013 2011-2012 2010-2011

Paolo SALANI

Paolo SALANI

Insegnamenti relativi all'Anno Accademico