Nonlinear fractional problems (Analisi di problemi frazionari non lineari)

Investigators: Agnese Di Castro (Universita degli Studi di Pisa), Serena Dipierro (School of Mathematics of Edimburgh), Giampiero Palatucci (P.I., SISSA Trieste).

Collaborators: Paolo Baroni (Uppsala), Alessio Figalli (Austin), Giovanni Franzina (Erlangen), Tuomo Kuusi (Aalto University), Adriano Pisante (Sapienza Roma), Yannick Sire (LATP Marseille), Enrico Valdinoci (WIAS Berlin)

Visitors:
  • Manuel Del Pino (Universidad de Chile), Pisa, February 17-23, 2014, [Talk: Examples of fractional minimal surfaces, February 20, 2014]
  • Maria del Mar Gonzalez (UPC Barcelona), Pisa, February 16-23, 2014, [Talk: The CR fractional Laplacian, February 21, 2014]
  • Adriano Pisante (Sapienza Universita di Roma), Parma, May 15-16, 2013 [Talk: Improved Sobolev embeddings and concentration-compactness for fractional Sobolev spaces, May 16, 2013]
  • Yannick Sire (LATP Marseille), SISSA, Jan 14-22, 2014 [Talk: Non local phase transitions and a non local version of De Giorgi conjecture, Jan 15, 2014]
  • Enrico Valdinoci (WIAS Berlin), Pisa, February 18-22, 2014 [Talk: Dislocation dynamics in crystals, February 21, 2014]

Visiting:
  • Paolo Baroni in Mittag-Leffler Institut, Stockholm, November 29 - December 13, 2013
  • Tuomo Kuusi in Aalto University, Helsinki, April 7-16, 2014

Events:

Seminars:
  • Serena Dipierro, Seminar on Differential Geometry and Analysis, Institut fur Analysis und Numerik, Magdeburg, Germany [Talk: Asymptotics of the nonlocal perimeter functionals, May 13, 2013]
  • Serena Dipierro, Department of Mathematics, University of Padova, Italy, [Talk: Asymptotics of fractional perimeter functionals, May 22, 2013]
  • Serena Dipierro, Spring School "Rate-independent evolutions and hysteresis modelling", Politecnico di Milano and University of Milano, Italy, [Talk: Asymptotics of fractional perimeter functionals, May 27, 2013]
  • S. Dipierro, G. Palatucci: Asymptotics of the nonlocal perimeter functionals - Recent advances in partial differential equations and applications, Milano, June 17--22, 2013. Also, in SIAM@PoliMI, Politecnico di Milano, June 28, 2013 - poster here
  • Serena Dipierro, Summer School "Non local equations of elliptic type", Palazzone di Cortona, Italy, [Talk: Asymptotics of fractional perimeter functionals, Jul 3, 2013]
  • Giampiero Palatucci, Dipartimento di Matematica, Università di Trento, Italy, [Talk: Disuguaglianze di Sobolev migliorate e concentrazione-compattezza per spazi di Sobolev frazionari, Nov 18, 2013]
  • Serena Dipierro, Seminar on Differential Geometry and Analysis, Universidad Autonoma de Madrid, Spain [Talk: Dislocation dynamics in crystals: a macroscopic theory in a fractional Laplace setting, Dec 11, 2013]
  • Giampiero Palatucci, Junior Analysis Seminars, SISSA, Trieste, Italy [Talk: Nonlocal perimeter functionals, Feb 5, 2014]
  • Serena Dipierro, Analysis Seminars, School of Mathematics, University of Edinburgh [Talk: Dislocation dynamics in crystals, Feb 10, 2014]
  • Giampiero Palatucci, Seminario di Equazioni Differenziali, Università di Tor Vergata, Roma, Italy [Talk: Sul comportamento locale delle estremali degli integrali non locali, Apr 8, 2014]
  • G. Palatucci, School of Science, Aalto University, Helsinki, Finland [Talk: Nonlocal perimeter functionals, Apr 14, 2014]

Pubblications:
  • J. Davila, M. del Pino, S. Dipierro, E. Valdinoci: Concentration phenomena for the nonlocal Schrodinger equation with Dirichlet datum - preprint here
  • A. Di Castro, T. Kuusi, G. Palatucci: Local behavior of fractional $p$-minimizers - preprint here
  • A. Di Castro, T. Kuusi, G. Palatucci: Nonlocal Harnack inequalities - preprint here
  • S. Dipierro: Asymptotics of fractional perimeter functionals - preprint here
  • S. Dipierro, A. Figalli, E. Valdinoci: Strongly nonlocal dislocation dynamics in crystals - Comm. Partial Differential Equations - preprint here.
  • S. Dipierro, G. Palatucci, E. Valdinoci: Dislocation dynamics in crystals: a macroscopic theory in a fractional Laplace setting - Comm. Math. Phys. - preprint here.
  • G. Franzina, G. Palatucci: Fractional $p$-eigenvalues - Riv. Mat. Univ. Parma - preprint here
  • G. Palatucci, A. Pisante: Improved Sobolev embeddings, profile decomposition, and concentration-compactness for fractional Sobolev spaces - Calc. Var. Partial Differential Equations - preprint here
  • G. Palatucci, A. Pisante, Y. Sire: Subcritical approximation of Yamabe type non local equation: a Gamma-convergence approach - Ann. Sc. Norm. Super. Pisa Cl. Sci. - preprint here
  • S. Dipierro, O. Savin, E. Valdinoci: All functions are locally $s$-harmonic up to a small error - preprint here

since May 9, 2013 - contact me