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:

- Tuomo Kuusi, in Parma, February 7--14 2015

- 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]

- G. Palatucci, “Nonlinear Partial Differential Equations and stochastic methods”, Jyvaskyla, Finland [Talk: Local behavior of fractional p-minimizers, Jun 10, 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]

- P. Baroni, “8th European conference on elliptic and parabolic problems”, Gaeta, Italy [Talk: A quantitative modulus of continuity in the two-phase Stefan problem, Jun 26-30, 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]

- P. Baroni, XXV Convegno Nazionale di Calcolo delle Variazioni, Levico T. (TN), Italy [Talk: Continuita del gradiente per minimi di funzionali non differenziabili, February 3, 2015]

- 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]

- G. Palatucci, Phase transition problems and nonlinear PDEs, University of Bologna, Italy [Talk: Dislocation dynamics in crystals, March 9, 2015] (scheduled)
- E. Cinti, Phase transition problems and nonlinear PDEs, University of Bologna, Italy [Talk: Flatness of nonlocal phase transition in low dimension, March 10, 2015] (scheduled)

- S. Dipierro, Phase transition problems and nonlinear PDEs, University of Bologna, Italy [Talk: All functions are locally s-harmonic up to a small error, March 11, 2015] (scheduled)

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*