Nonlocal equations, norms and operators (Operatori, norme ed equazioni non locali)

Investigators: Paolo Baroni (Uppsala), Eleonora Cinti (WIAS - Berlin), Agnese Di Castro (P.I., SBAI - Sapienza Universita di Roma), Serena Dipierro (School of Mathematics of Edimburgh), Giampiero Palatucci (Universita degli Studi di Parma).

Collaborators: Manuel del Pino (Universidad de Chile), Maria del Mar Gonzalez (UPC Barcelona), Tuomo Kuusi (Aalto University), Adriano Pisante (Sapienza Roma), Yannick Sire (LATP Marseille), Enrico Valdinoci (WIAS Berlin / University of Milano)

Visitors:
  • Enrico Valdinoci, in Bologna, March 5--13 2015 (scheduled)

Visiting:
  • [P. Baroni]: T. Kuusi in Aalto University, Helsinki, Finland, May 16-23, 2014
  • [P. Baroni]: P. Lindqvist in Trondheim, Norway, November 30, 2014 - December 5, 2014
  • [S. Dipierro]: O. Savin in Columbia University, USA, March 30 - April 14, 2014
  • [A. Di Castro, G. Palatucci]: T. Kuusi in Aalto University, Helsinki, Finland, April 9-17, 2014
  • [S. Dipierro]: M. del Pino in Universidad de Chile, Santiago, Chile, July 10 - August 8, 2014
  • [G. Palatucci]: A. Di Castro in Sapienza University of Roma, Italy, November 20-29, 2014

Seminars:
  • G. Palatucci, Seminario di Equazioni Differenziali, Università di Tor Vergata, Roma, Italy [Talk: Sul comportamento locale delle estremali degli integrali non locali, Apr 8, 2014]
  • S. Dipierro, Department of Mathematics, Columbia University, New York, USA [Talk: Concentration phenomena for the nonlocal Schrodinger equation, Apr 10, 2014]
  • G. Palatucci, School of Science, Aalto University, Helsinki, Finland [Talk: Nonlocal perimeter functionals, Apr 14, 2014]
  • E. Cinti, Universidad Autonoma de Madrid, Spain [Talk: A quantitative weighted isoperimetric inequality via the ABP method, May, 2014]
  • P. Baroni, School of Science, Aalto University, Helsinki, Finland [Talk: A quantitative modulus of continuity in the two-phase Stefan problem, May 21, 2014]
  • G. Palatucci, Seminario di Analisi Matematica, Dipartimento SBAI, Sapienza Università di Roma, Italy [Talk: Sul comportamento locale delle estremali degli integrali non locali, May 23, 2014]
  • E. Cinti, “Women in Partial Differential Equations and Calculus of Variations Workshop", Mathematical Institute, University of Oxford, UK [Talk: The isoperimetric problem with density, Jun, 2014]
  • E. Cinti, “Isoperimetric problems between Analysis and Geometry", SNS Pisa, Italy [Talk: A quantitative weighted isoperimetric inequality via the ABP method, Jun, 2014]
  • G. Palatucci, INdAM Meeting “Singular and degenerate evolution problems”, Cortona, Italy [Talk: Dislocation dynamics in crystals, Jun 26, 2014]
  • E. Cinti, AIMS Conference Series on Dynamical Systems and Differential Equations, Instituto de Ciencias Matematicas and UAM Madrid, Spain [Talk: Phase transitions in Stein manifolds and boundary energies, July, 2014]
  • E. Cinti, AIMS Conference Series on Dynamical Systems and Differential Equations, Instituto de Ciencias Matematicas and UAM Madrid, Spain [Talk: A Liouville-type result for a nonlinear and nonlocal equation in the Heisenberg group, July, 2014]
  • S. Dipierro, AIMS Conference Series on Dynamical Systems and Differential Equations, Instituto de Ciencias Matematicas and UAM Madrid, Spain [Talk: Concentration phenomena for the nonlocal Schrodinger equation, July, 2014]
  • S. Dipierro, AIMS Conference Series on Dynamical Systems and Differential Equations, Instituto de Ciencias Matematicas and UAM Madrid, Spain [Talk: Dislocation dynamics in crystals, July, 2014]
  • S. Dipierro, Analysis seminars, Heriot-Watt University, Edinburgh, UK [Talk: Nonlocal problems with Neumann boundary conditions, October 2, 2014]
  • P. Baroni, Mathematical institute, University of Oxford, UK [Talk: Continuous solutions to the degenerate Stefan problem, October 20, 2014]
  • E. Cinti, Universitat Politecnica de Catalunya, Spain [Talk: A quantitative weighted isoperimetric inequality via the ABP method, November, 2014]
  • E. Cinti, Workshop PDE’s and Global Analysis @UniMI, University of Milano, Italy [Talk: A quantitative weighted isoperimetric inequality via the ABP method, November 27, 2014]
  • A. Di Castro, Workshop PDE’s and Global Analysis @UniMI, University of Milano, Italy [Talk: Local behavior of fractional minimizers, November 28, 2014]
  • P. Baroni, Dept. of Mathematical Sciences, NTNU, Trondheim [Talk: Regularity results for a class of non-autonomous functionals in a borderline case, December 2, 2014]
  • G. Palatucci, Dipartimento di Matematica, University of Milano, Italy [Talk: Dislocation dynamics in crystals, December 3, 2014]
  • P. Baroni, Analysis and Stochastics Seminar, Dept. of Mathematics, Uppsala University [Talk: Continuous solutions to the degenerate Stefan problem, December 9, 2014]
  • S. Dipierro, Department of Mathematics, University of Turin, Italy [Talk: A nonlocal free boundary problem, December 11, 2014]
  • G. Palatucci, “Nonlocal days”, Basel, Switzerland [Talk: Local behavior of fractional minimizers, December 16, 2014]
  • E. Cinti, University of Bonn, Germany [Talk: A quantitative weighted isoperimetric inequality via the ABP method, Feb, 2015]
  • S. Dipierro, School of Mathematics, Cardiff University, UK [Talk: Dislocation dynamics in crystals: nonlocal effects and a macroscopic theory in a fractional Laplace setting, February 9, 2015]

Pubblications and preprints:
  • P. Baroni: Marcinkiewicz estimates for degenerate parabolic equations with measure data - J. Funct. Anal.
  • P. Baroni, A. Di Castro, G. Palatucci: Anisotropic De Giorgi classes - preprint here
  • P. Baroni, M. Colombo, G. Mingione: Non-autonomous functionals, borderline cases and related function classes - St. Petersburg Math. J.
  • P. Baroni, M. Colombo, G. Mingione: Harnack inequalities for double phase functionals - Nonlinear Anal.
  • P. Baroni, T. Kuusi, G. Mingione: Borderline gradient continuity of minima - J. Fixed Point Theory Appl.
  • E. Cinti, J. Tan: A nonlinear Liouville theorem for fractional equations in the Heisenberg group - preprint here
  • E. Cinti, A. Pratelli: The $\varepsilon-\varepsilon^\beta$ property and the boundedness of isoperimetric sets in $\R^N$ with density - J. Reine Angew. Math. (Crelle’s Journal - preprint here
  • J. Davila, M. del Pino, S. Dipierro, E. Valdinoci: Concentration phenomena for the nonlocal Schrodinger equation with Dirichlet datum - preprint here
  • J. Davila, M. del Pino, S. Dipierro, E. Valdinoci: Nonlocal Delaunay surfaces - preprint here
  • A. Di Castro, J. Korvempaa, T. Kuusi, G. Palatucci: Nonlocal superminimizers - 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 - J. Funct. Anal. - preprint here
  • A. Di Castro, M. Novaga, B. Ruffini, E. Valdinoci: Nonlocal isoperimetric problems - preprint here
  • S. Dipierro: Asymptotics of fractional perimeter functionals and related problems - preprint here
  • S. Dipierro, M. Medina, I. Peral, E. Valdinoci: Bifurcation results for a fractional elliptic equation with critical exponent in R^n - preprint here
  • S. Dipierro, A. Figalli, E. Valdinoci: Strongly nonlocal dislocation dynamics in crystals - Comm. Partial Differential Equations - preprint here
  • S. Dipierro, O. Savin, E. Valdinoci: All functions are locally s-harmonic up to a small error - JEMS - preprint here
  • S. Dipierro, O. Savin, E. Valdinoci: A nonlocal free boundary problem - preprint here
  • S. Dipierro, X. Ros-Oton, E. Valdinoci: Nonlocal problems with Neumann boundary conditions - preprint here
  • S. Dipierro, E. Valdinoci: On a fractional harmonic replacement - DCDS - preprint here
  • S. Dipierro, E. Valdinoci: A density property for fractional weighted Sobolev spaces - preprint here
  • G. Palatucci, A. Pisante: A Global Compactness type result for Palais-Smale sequences in fractional Sobolev spaces - Nonlinear Anal. - preprint here


INdAM GNAMPA Project 2014

since March 12, 2014 - contact me