Teaching

• Analisi Vettoriale - 2023/2024 - tutte le informazioni saranno reperibili sulla pagina elearning del corso
  

• Equazioni Differenziali - 2023/2024 - tutte le informazioni saranno reperibili sulla pagina elearning del corso

• Analisi Vettoriale - 2022/2023 - tutte le informazioni sono reperibili sulla pagina elearning del corso
  

• Matematica III - 2022/2023 - tutte le informazioni sono reperibili sulla pagina elearning del corso

Scientific interests

• Elliptic and parabolic Nonlinear PDEs

• Variational methods in Nonlinear Analysis

• Liouville-type equations and systems

Publications

• F. De Marchis, Multiplicity result for a scalar field equation on compact surfaces, Comm. Partial Differential Equations 33/10-12 (2008), 2208-2224.

• F. De Marchis, Generic multiplicity for a scalar field equation on compact surfaces, J. Funct. Anal. 259/8 (2010), 2165-2192.

• F. De Marchis, Multiplicity of solutions for a mean field equation on compact surfaces, Boll. U.M.I. 4/2 (2011), 245-257.

• D. Bartolucci, F. De Marchis, A. Malchiodi, Supercritical conformal metrics on surfaces with conical singularities, Int. Mat. Res. Not. 24 (2011), 5625-5643.
  

• F. De Marchis, Existence and multiplicity of solutions for problems in Geometrical Analysis, Ph.D. Thesis, SISSA Trieste, 2010.

• D. Bartolucci, F. De Marchis, On the Ambjorn-Olesen Electroweak condensates, J. Math. Phys. 53/7 (2012), 073704, 15 pp.
  

• F. De Marchis, I. Ianni, F. Pacella, Sign changing solutions of Lane Emden problems with interior nodal line and semilinear heat equations, J. Differential Equations 254/8 (2013), 3596-3614.

• F. De Marchis, I. Ianni, Blow up of solutions of semilinear heat equations in non radial domains of R^2, Discrete and Contin. Dyn. Systems - A 35/3 (2015), 891-907.

• F. De Marchis, I. Ianni, F. Pacella, Asymptotic analysis and sign changing bubble towers for Lane-Emden problems, J. Eur. Math. Soc. 17 (2015), 2037-2068.

• D. Bartolucci, F. De Marchis, Supercritical mean field equations on convex domains and the Onsager's statistical description of two dimensional turbulence, Arch. Ration. Mech. Anal. 217/2 (2015), 525-570.

• F. De Marchis, I. Ianni, F. Pacella, Morse index and sign changing bubble towers for Lane-Emden problems, Ann. Mat. Pura Appl., 195/2 (2016), 357-369.

• F. De Marchis, I. Ianni, F. Pacella, Exact Morse index computation for nodal radial solutions of Lane-Emden problems, Math. Annalen 367 (2017), no. 1, 185-227.

• F. De Marchis, R. Lopez Soriano, Existence and non existence results for the singular Nirenberg problem, Calc. Var. Partial Differential Equations 55 (2016), no.2, Art. 36, 35 pp.

• F. De Marchis, I. Ianni, F. Pacella, Asymptotic profile of positive solutions of Lane-Emden problems in dimension two, J. Fix. Point Theory A. 19 (2017), no.1, 889-916.

• F. De Marchis, I. Ianni, F. Pacella, A Morse index formula for radial solutions of Lane-Emden problems, Adv. Math 322 (2017), 682-737.

• F. De Marchis, T. Ricciardi, Existence results for turbulent flows with arbitrary intensities, Nonlinear Anal. Real. 38 (2017) 222–244.

• F. De Marchis, R. Lopez Soriano, D. Ruiz, Compactness, existence and multiplicity for the singular mean field problem with sign-changing potentials, J. Math. Pure Appl. 115 (2018), 237-267.

• F. De Marchis, I. Ianni, F. Pacella, Asymptotic analysis for the Lane-Emden problem in dimension two, contribution to the volume Partial Differential Equations arising from Physics and Geometry, London Mathematical Society (No. 450), Cambridge University Press (2018).

• T. D'Aprile, F. De Marchis, I. Ianni, Prescribed Gauss curvature problem on singular surfaces, Calc. Var. PDE 57 (2018), doi: s00526-018-1373-3.

• F. De Marchis, M. Grossi, I. Ianni, F. Pacella, L^oo-norm and energy quantization for the planar Lane-Emden problem with large exponent, Archiv der Mathematik 111 (2018), 421–429.

• F. De Marchis, M. Grossi, I. Ianni, F. Pacella, Morse index and uniqueness of positive solutions of the Lane-Emden problem in planar domains, Journal de Mathématiques Pures et Appliquées 128 (2019), 339-378.
  
  
• A. Amadori, F. De Marchis, I. Ianni, Morse index computation for radial solutions of the Hénon problem in the disk, Nonlinear Analysis, Theory, Methods and Applications, 2022, 215, 112645.

• F. De Marchis, A. Malchiodi, L. Martinazzi, P.D. Thizy, Critical points of the Moser-Trudinger functional on closed surfaces, Inventiones 230 (2022), 1165-1258.
  
  
• F. De Marchis, H. Fourti, I. Ianni, Sharp boundary concentration for a two-dimensional nonlinear Neumann problem, submitted 2023.
  

Previous positions and awards

• 2017-2020:  Assistant Professor (RTD-B) at Mathematics Department, University of Rome "Sapienza"

• 2014-2017:  Post-doc at Mathematics Department, University of Rome "Sapienza"

• 2012-2014:  Post-doc at Mathematics Department, University of Rome "Tor Vergata"
  

• 2011-2012:  Post-doc at Mathematics Department, University of Rome "Sapienza"
  

• 2011:  Prize for Doctors in Mathematics (in memory of Michele Cuozzo), University of Rome "Tor Vergata"

• 2011:  Post-doc fellowship, awarded by INDAM (declined)
  

• 2007-2010:  Three-years fellowship for Ph.D. course in Mathematical Analysis, instituted by SISSA

• 2005-2007:  Two-years fellowship for Master's Degree in Mathematics, instituted by SISSA
  

• 2005:  “Cesare e Giustina Labonia” Graduation Prize for the best female graduate student in Mathematics in Rome, awarded by FILDIS

• 2005:  Prize for the best graduate student in Mathematics, awarded by the Department of Mathematics of University of Rome "Sapienza"

• 2002-2005:  Three-years fellowship for Bachelor's Degree in Mathematics, instituted by INDAM
  

Grants

• 2021:  Principal Investigator of the research project "Nonlinear PDEs: from geometry to population dynamics", , University of Rome "Sapienza"
  
  
• 2018:  Principal Investigator of the research project "Elliptic equations and systems arising in Geometry and Physics", University of Rome "Sapienza"
  
  
• FFABR (Fondo per il Finanziamento delle Attività Base di Ricerca)  2017, Anvur

• 2016:  Principal Investigator of the research project "Nonlinear problems with geometrical or physical motivations", Avvio alla Ricerca 2016, University of Rome "Sapienza"
  

• 2015:  Principal Investigator of the research project "Partial differential equations with power and exponential nonlinearities", Avvio alla Ricerca 2015, University of Rome "Sapienza"

• 2014:  Principal Investigator of the research project "Fenomeni di esplosione per problemi parabolici semilineari", GNAMPA 2014, INDAM
  

Curriculum Vitae