RESEARCH INTERESTS

Daniele Bartolucci

E-mail: bartoluc - at - mat - dot - uniroma2 - dot - it

D. Bartolucci Home Page 


  • Blow-up analysis and pointwise estimates for Liouville type equations with singular data. Self-dual vortices in Gauge theories.
    Existence of solutions of systems of P.D.E. of Liouville type with and without singular data.
    Main references:
    D. Bartolucci, G. Tarantello, Comm. Math. Phys. 229 (2002); DOI:10.1007/s002200200664
    D. Bartolucci, G. Tarantello, J. D. E. 185 (2002); DOI:10.1006/jdeq.2001.4159
    D. Bartolucci, Nonlinear Analysis: T.M.A. 53 (2003); DOI:10.1016/S0362-546X(02)00310-3
    D. Bartolucci, C.C. Chen, C.S. Lin, G.Tarantello, Comm. in P. D. E., 29 (2004); DOI: 10.1081/PDE-200033739
    D. Bartolucci, F. De Marchis, Jour. Math. Phys. 53 (2012); DOI:10.1063/1.4731239
    D. Bartolucci, Y. Lee, C.S. Lin, M. Onodera, A. I. H. P.: An. Non Lin. 32 (2015); DOI:10.1016/j.anihpc.2014.03.001
    D. Bartolucci, Calc. Var. & P.D.E., 53 (2015); DOI: 10.1007/s00526-014-0750-9
    D. Bartolucci, D. Castorina, Comm. Contemp. Math. 18 (2016); DOI:10.1142/S0219199715500686
    D. Bartolucci, G. Tarantello, J.D.E. 262 (2017); DOI:10.1016/j.jde.2016.12.003

  • The prescribing Gaussian curvature problem on surfaces with conical singularities. Improved Moser-Trudinger type inequalities.
    Best pinching constants on S^2 with conical singularities. Uniqueness of convex polytopes.
     Main references:
    D. Bartolucci, F. De Marchis, A. Malchiodi, Int. Math. Res. Not. 24 (2011); DOI: 10.1093/imrn/rnq285.
    D. Bartolucci, Jour. Geom. Analysis 23 (2013); DOI: 10.1007/s12220-011-9266-0.
    D. Bartolucci, A. Malchiodi, Comm. Math. Phys. 322 (2013); DOI: 10.1007/s00220-013-1731-0.
    D. Bartolucci, D. Castorina, Ann. Scuola Norm. Sup. Pisa Cl. Sci. XIX (2019);
    D. Bartolucci, C. Gui, A. Jevnikar, A. Moradifam,  Math. Ann. 374 (2019).

  • Existence, uniqueness and local uniqueness of solutions of mean-field type equations.
    The Onsager statistical mechanics description of 2D turbulent Euler flows. Global and local bifurcation analysis.
     Main references:
    D. Bartolucci, C.S. Lin, Comm. in P.D.E. 34 (2009); DOI: 10.1080/03605300902910089
    D. Bartolucci, Calc. Var. & P.D.E. 38 (2010); DOI: 10.1007/s00526-009-0296-4
    D. Bartolucci, C.S. Lin, G. Tarantello, Comm. Pure Appl. Math. 64 (2011); DOI: 10.1002/cpa.20385
    D. Bartolucci, C.S. Lin, J.D.E. 252 (2012); DOI: 10.1016/j.jde.2011.12.014
    D. Bartolucci, C.S. Lin, Math. Ann. 359 (2014); DOI:10.1007/s00208-013-0990-6
    D. Bartolucci, F. De Marchis, A.R.M.A. 217 (2015); DOI: 10.1007/s00205-014-0836-8
    D. Bartolucci, Calc. Var. & P.D.E. 58 (2019); DOI: 10.1007/s00526-018-1445-4
    D. Bartolucci, A. Jevnikar, Y. Lee, W. Yang, Jour. Math. Pure App. 123 (2019);
    D. Bartolucci, A. Jevnikar, Y. Lee, W. Yang, A.R.M.A. 230 (2018); DOI: 10.1007/s00205-014-0836-8;
    D. Bartolucci, A. Jevnikar, C.S. Lin, J.D.E. 266 (2019); DOI: 10.1016/j.jde.2018.07.053
    D. Bartolucci, A. Jevnikar, Y. Lee, W. Yang,  C.P.D.E. 44 (2019);
    D. Bartolucci, C. Gui, A. Jevnikar, Y. Hu, W. Yang, "Mean field equations on tori: existence and uniqueness of evenly symmetric blow-up solutions" to appear on D.C.D.S.;
    D. Bartolucci, A. Jevnikar, "On the global bifurcation diagram of the Gel'fand problem", Preprint 2019, ArXiv:1901.06700v1;
    D. Bartolucci, A. Jevnikar, Y. Lee, W. Yang "Local uniqueness and non-degeneracy of blow up solutions of mean field equations with singular data", Preprint (2019).

  • Harnack-type inequalites for blow-up solutions of Liouville type equations with singular data and of uniformly elliptic Liouville type equations.
     Main references:
    D. Bartolucci, L. Orsina, Asymptotic Analysis 58 (2008); DOI: 10.3233/ASY-2008-0879
    D. Bartolucci, L. Orsina, Adv. Nonlinear Studies 10 (2010);
    D. Bartolucci, Proc. Royal Soc. of Edinburgh 140A (2010); DOI: 10.1017/S0308210509000596
    D. Bartolucci, Jour. d'Analyse Math. 117 (2012); DOI: 10.1007/s11854-012-0013-7
    D. Bartolucci, Jour. Math. Anal. Appl. 403 (2013); DOI: 10.1016/j.jmaa.2013.02.051

  • Existence and qualitative properties of solutions of Liouville and sinh-Poisson problems.
     D. Bartolucci, E. Montefusco, Nonlinearity 19 (2006); DOI: 10.1088/0951-7715/19/3/005
    D. Bartolucci, E. Montefusco, Math. Meth. in Appl. Sci. 30 (2007); DOI: 10.1002/mma.887
    D. Bartolucci, A. Pistoia, I.M.A. Jour. of Appl. Math. 72 (2007); DOI: 10.1093/imamat/hxm012
    D. Bartolucci, Acta Appl. Math. 110 (2010); DOI: 10.1007/s10440-008-9376-2

  • The Emden-Fowler equation with exponential nonlinearity in two and higher dimensions.
    Blow up analysis and equilibrium configurations of plasmas and selfgravitating objects.
     Main references:
    D. Bartolucci, F. Leoni, L. Orsina, A.C. Ponce, A. I. H. P.: An. Non Lin. 22 (2005);
    D. Bartolucci, F. Leoni, L. Orsina, Comm. Contemp. Math. 9 (2007); DOI: 10.1142/S0219199707002411
    D. Bartolucci, Int. Jour. Mod. Phys. D, 21 (2012); DOI:10.1142/S0218271812500873
    D. Bartolucci, G. Wolansky, "Maximal entropy solutions under prescribed mass and energy", Preprint 2018.


  • Some recent papers in collaboration with or by G. Tarantello.
     D. Bartolucci, G. Tarantello, ASYMPTOTIC BLOW-UP ANALYSIS FOR SINGULAR LIOUVILLE TYPE EQUATIONS WITH APPLICATIONS;
    G. Tarantello, Blow-up analysis for a cosmic strings equation;
    A. Poliakovsky, G. Tarantello, On non-topological solutions for planar Liouville Systems of Toda-type;
    Y. LEE, C.S. LIN, G. TARANTELLO, W. YANG, SHARP ESTIMATES FOR SOLUTIONS OF MEAN FIELD EQUATION WITH COLLAPSING SINGULARITY.

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