P(n)/N(p)

P(n)/N(p) : Problemi differenziali nonlineari/Nonlinear differential problems

2024/25 Seminars

• 28 Novembre 2024, ore 14,30, sala di Consiglio
  Luigi Pollastro (Università di Torino)
  A case for the logarithmic Laplacian
  In the past few decades the fractional Laplacian (-\Delta)^s has capitalized the attention of the PDE community as an integrodifferential operator which is the nonlocal counterpart to the classical Laplacian. Gaining popularity thanks to the seminal work of L. Caffarelli & L. Silvestre "An extension problem related to the fractional Laplacian", it sees a widespread use thanks to its ability to model phenomena in which long term interactions between objects occur, leading to applications in particle physics, finance and population dynamics among others. An interesting line of research is to investigate what happens to the operator as the index s approaches 0. It is in this instance that the logarithmic Laplacian pops up, as the first order term in the Taylor expansion of the fractional Laplacian as s goes to 0. The goal of this seminar is to present this fairly new operator, showcasing its basic features together with some open questions. Lastly, I will present symmetry results for an overdetermined and a rigidity problem involving the logarithmic Laplacian recently obtained in collaboration with N. Soave.
  
  
  
  

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  Future talks

  • 12 Dicembre 2024
    Stefano Vita (Università di Pavia)
    
  
  
  
  
  
  

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  Past talks

  • 5 Ottobre 2023
    Clara Patriarca (Politecnico di Torino)
    Attractors for a fluid-structure interaction problem in a time-dependent phase space
  
  
  
  • 19 Ottobre 2023
    Lele Du (Sapienza Università di Roma)
    On elliptic equations with Stein-Weiss type convolution parts
  
  
  
  • 9 Novembre 2023
    Francesca Corni (Università di Bologna)
    The fractional powers of the sub-Laplacian in Carnot groups through an analytic continuation
  
  
  
  • 23 Novembre 2023
    Francesca Da Lio (ETH, Zurich)
    Integrability by Compensation and Morse Index Stability for Conformally Invariant Variational Problems in 2D
  
  
  
  • 7 Dicembre 2023
    Danilo Gregorin Afonso (Sapienza Università di Roma)
    Semilinear elliptic equations under geometric constraints: energy instability and overdetermined problems
  
  
  
  • 18 Gennaio 2024
    Paolo Piccione (Universidade de Sao Paulo)
    Algebraic and topological methods for Yamabe-type problems
  
  
  
  • 1 Febbraio 2024
    Carlo Mercuri (Università di Modena e Reggio Emilia)
    Solutions to nonlinear elliptic problems involving Sobolev exponent
  
  
  
  • 15 Febbraio 2024
    Dario Daniele Monticelli (Politecnico di Milano)
    Nonexistence results for some elliptic equations on infinite graphs
  
  
  
  • 29 Febbraio 2024
    Riccardo Molle (Università di Roma Tor Vergata)
    Limit profiles for normalized solutions to Gross-Pitaevskii-Poisson equations
  
  
  
  • 14 Marzo 2024
    Fabio Punzo (Politecnico di Milano)
    A general nonlinear characterization of stochastic incompleteness
  
  
  
  • 4 Aprile 2024
    Giulio Tralli (Università di Ferrara)
    Overdetermined problems tailored for gauge balls
  
  
  
  • 18 Aprile 2024
    Marco Pozza (Link Campus University)
    Homogenization of Hamilton-Jacobi Equations posed on Networks
  
  
  
  • 2 Maggio 2024
    Shuhei Kitano (Waseda University, Tokyo)
    Calderón-Zygmund estimates for fully nonlinear nonlocal equations
  
  
  
  • 16 Maggio 2024
    Luigi Muglia (Università della Calabria)
    Optimal second order boundary regularity for solutions to p-Laplace equations
  
  
  
  • 30 Maggio 2024
    Francesco Della Pietra (Università di Napoli Federico II)
    Problemi di ottimizzazione di forma in modelli per la trasmissione del calore
  
  
  
  • 6 Giugno 2024
    Andrea Davini (Sapienza Università di Roma)
    Stochastic Homogenization of viscous HJ equations in 1d
  
  
  
  • 26 Settembre 2024
    Pengfei Guan (McGill University, Montreal)
    A generalized mean curvature type flow and isoperimetric problem
  
  
  
  • 17 Ottobre 2024
    Paolo Cosentino (Università di Roma Tor Vergata)
    A Harnack type inequality for singular Liouville type equations
  
  
  
  • 31 Ottobre 2024
    Roberta Filippucci (Università degli Studi di Perugia)
    Pointwise a priori estimates and nonexistence results for problems with gradient terms
  
  
  

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