Andrea Bonfiglioli

       Assistant Professor of Mathematical Analysis

Dipartimento di Matematica
Universita' degli Studi di Bologna
P.zza di Porta S. Donato, 5
40126 - Bologna - Italy
phone : +39-051-2094498 Fax +39-051-2094490
email address: andrea.bonfiglioli6@unibo.it


Scientific interests:

Second order linear partial differential equations with non-negative characteristic form. Potential Theory. Lie groups and Lie algebras. Real analysis.

  • Papers

    •     Complete list (published papers, preprints, in progress): pdf

        Main list (published papers):

    1. Liouville-type theorems for real sub-Laplacians (con E. Lanconelli) Manuscripta Math. 105, 111--124 (2001).
    2. Expansion of the Heisenberg integral mean via iterated Kohn Laplacians: a Pizzetti-type formula, Pot. Analysis 17, 165--180 (2002).
    3. Maximum Principle on unbounded domains for sub-Laplacians: a Potential Theory approach (con E. Lanconelli), Proc. Amer. Math. Soc. 130, 2295--2304 (2002).
    4. Subharmonic functions on Carnot groups (con E. Lanconelli), Math. Ann. 325, 97--122 (2003).
    5. Uniform Gaussian estimates of the fundamental solutions for heat operators on Carnot groups (con E. Lanconelli, F. Uguzzoni), Adv. Differential Equations 7 (2002), 1153-1192.
    6. Nonlinear Liouville theorems for some critical problems on H-type groups (con F. Uguzzoni), J. Funct. Anal. 207 (2004), 161-215.
    7. Levi's parametrix for some sub-elliptic non-divergence form operators (con E. Lanconelli, F. Uguzzoni), Electron. Res. Announc. Math. Sci. 9 (2003), 10-18.
    8. Some non-existence results for critical equations on step-two stratified groups (con F. Uguzzoni), C. R. Acad. Sci. Paris Ser. I Math. 336 (2003), 817-822.
    9. Homogeneous Carnot groups related to sets of vector fields, Bollettino U.M.I. (8) 7-B (2004), 79-107.
    10. Families of diffeomorphic sub-Laplacians and free Carnot groups (con F. Uguzzoni), Forum Math. 16 (2004), 403--415.
    11. A note on lifting of Carnot groups (con F. Uguzzoni), Rev. Mat. Iberoamericana 21 (2005), 1013--1035.
    12. Fundamental solutions for non-divergence form operators on stratified groups (con E. Lanconelli, F. Uguzzoni), Trans. Amer. Math. Soc. (2004), 356, 2709--2737.
    13. A Poisson-Jensen type representation formula for subharmonic functions on stratified Lie groups (con C. Cinti), Pot. Analysis 22 (2005), 151--169.
    14. Representation formulas and Fatou-Kato theorems for heat operators on stratified groups (con F. Uguzzoni) Rendiconti di Matematica, Serie VII, 25, 53--67 (2005).
    15. The theory of energy for sub-Laplacians with an application to quasi-continuity (con C. Cinti) Manuscripta Math. (2005), 118, 283--309.
    16. Maximum principle and propagation for intrinsicly regular solutions of differential inequalities structured on vector fields (con F. Uguzzoni) J. Math. Anal. Appl. (2006), 322, 886--900.
    17. Dirichlet problem with L^p-boundary data in contractible domains of Carnot groups (con E. Lanconelli), Ann. Sc. Norm. Super. Pisa, Cl. Sci. 5 (2006), 579--610.
    18. Harnack inequality for non-divergence form operators on stratified groups (con F. Uguzzoni) Trans. Amer. Math. Soc. (2007), 359, 2463--2481.
    19. Gauge functions, Eikonal equations and Bocher's theorem on stratified Lie groups (con E. Lanconelli) Calc. Var. Partial Diff. Equations (2007), 30, 277--291.
    20. Stratified Lie Groups and Potential Theory for their sub-Laplacians, Monografia (con E. Lanconelli, F. Uguzzoni), Springer Monographs in Mathematics, 26. New York, NY: Springer-Verlag, 2007 (800 pagine).
    21. Taylor formula for homogeneous groups and applications, Math. Z. (2009), 262, 255--279.
    22. On left invariant Hormander operators in RN. Applications to Kolmogorov-Fokker-Planck equations (con E. Lanconelli), Journal of Mathematical Sciences, 171, n.1, 22--33 (2010).
    23. Pizzetti's formula for H-type groups, Potential Analysis (2009), 31, 311--333.
    24. Lifting of convex functions on Carnot groups and lack of convexity for a gauge function, Archiv der Mathematik (2009) 93, 277--286.
    25. An ODE's version of the formula of Baker, Campbell, Dynkin and Hausdorff and the construction of Lie groups with prescribed Lie algebra, Mediterr. J. Math. (2010), 7, 387--414.
    26. On left-invariant Hormander operators in R^N: applications to the Kolmogorov-Fokker-Planck equations (Russian) (con E. Lanconelli), Sovrem. Mat. Fundam. Napravl., 36, 24--35 (2010).
    27. Lie groups related to Hormander operators and Kolmogorov-Fokker-Planck equations (con E. Lanconelli), Commun. Pure Appl. Anal., 11, 1587--1614 (2012).
    28. Topics in Noncommutative Algebra. The Theorem of Campbell,  Baker, Hausdorff and Dynkin (con R. Fulci), Lecture Notes in Mathematics, vol. 2034, Springer-Verlag (2012) (XXII pages Introduction + 498 pages). ISBN 978-3-642-22596-3
    29. Subharmonic functions in sub-Riemannian settings (con E. Lanconelli), J. Eur. Math. Soc., 15, 387--441 (2013). Doi:10.4171/JEMS/364
    30. A new characterization of convexity in free Carnot groups (con E. Lanconelli), Proc. Amer. Math. Soc., 140, 3263--3273 (2012).
    31. A new  proof of the existence of free Lie algebras and an application (con R. Fulci), ISRN Algebra, vol. 2011 (2011). Article id 247403. doi:10.5402/2011/247403
    32. Matrix exponential groups and Kolmogorov-Fokker-Planck equations (con E. Lanconelli), J. Evol. Equ., 12, 59--82 (2012).
    33. H-convex distributions in stratified groups (con E. Lanconelli, V. Magnani, M. Scienza), to appear in Proc. Amer. Math. Soc. (2012). Il titolo è visibile nella sezione Articles in Press all'url: http://www.ams.org/cgi-bin/mstrack/accepted_papers?jrnl=proc
    34. The early proofs of the Theorem of Campbell, Baker, Hausdorff and Dynkin (con R.Achilles), Arch. Hist. Exact Sci., 66, 295--358 (2012).
    35. On the Dirichlet problem and the inverse mean value theorem for a class of divergence form operators (con B. Abbondanza), J. London Math. Soc., 87, 321--346 (2013). Doi: 10.1112/jlms/jds050.
    36. Convexity of average operators for subsolutions to subelliptic equations (con E. Lanconelli, A. Tommasoli), to appear in Analysis and PDE (2013).
    37. Normal families of functions for subelliptic operators and the theorems of Montel and Koebe (con. E. Battaglia), J. Math. Anal. Appl., 409, 1--12 (2014).
    38. On the convergence of the Campbell-Baker-Hausdorff-Dynkin series in infnite-dimensional Banach-Lie algebras (con S. Biagi), to appear in Linear and Multilinear Algebra (2013).

      39. Pre-Prints and Submitted Papers: 

    39. Finite-dimensional Lie algebras of complete Hörmander vector elds and applications (con S. Biagi), submitted (2013).

      In preparation:

    1. The contribution of Ernesto Pascal to the so-called Campbell-Hausdorff formula, In preparation (2012).
    2. Notions of Curvature: From the Riemannian to the sub-Riemannian case (con E. Lanconelli,  V. Martino, A. Montanari), Monografia, In preparation (2011).
    3. An Introduction to Subelliptic Laplacians, Monograph in preparation (2013).

  • Curriculum Vitae: pdf

  • Teaching

  • Courses

    • - Analisi Superiore 2, Corso di Laurea Magistrale in Matematica, Bologna

    - Istituzioni di Matematica 2, Corso di Laurea in Scienze Ambientali, Ravenna link


  • Teaching books

    • - Manuale di LaTeX (a cura di A. Bonfiglioli e C. Cinti), in preparazione (300 pagine circa) Bologna, 2009.

    - Istituzioni di Matematica 2, Teoria ed Esercizi, in preparazione (500 pagine circa) Bologna, 2008.

    Last updated January 2012
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