GNAMPA Project 2012Metodi variazionali per lo studio di equazioni ellittiche non-locali con operatori di tipo laplaciano frazionario
Collaborators: Adriano Pisante (Sapienza Roma), Begona Barrios (UAM Madrid), Edoardo Colorado (UC3M Madrid), Serena Dipierro (SISSA Trieste), Alessio Fiscella (Univ. Milano), Tuomo Kuusi (Aalto University), Giovanni Molica Bisci (Univ. Mediterranea Reggio Calabria), Yannick Sire (LATP Marseille), Enrico Valdinoci (Univ. Milano)
Workshops and Schools:
- Two days on Nonlocal Operators and Applications (partially sponsored)
Visitors:
- Yannick Sire (LATP Marseille), Parma, September 30 -- October 7, 2012. [Lectures: Non local problems: existence, regularity and qualitative properties, October 1-3-4, 2012. Talk: Ginzburg-Landau and fractional harmonic maps, October 6, 2012].
- Tuomo Kuusi (Aalto University), Parma, March 17 -- 23, 2013. [Talk: Local behavior of fractional p-minimizers, March 18, 2013].
Seminars:
- Raffaella Servadei, “7th European conference on elliptic and parabolic problems”, Gaeta, Parma [Talk: Fractional Laplacian equations with subcritical and critical growth, May 21, 2012].
- Raffaella Servadei, “Workshop on nonlinear partial differential equations”, Perugia [Talk: A variational approach to fractional Laplace equations, May 28, 2012].
- Raffaella Servadei, “Variational and topological methods”, Flagstaff AZ [Talk: Nonlocal equations of elliptic type: a variational approach, June 6, 2012].
- Raffaella Servadei, “The 9th AIMS conference on dynamical systems, differential equations and applications”, Orlando FL [Talk: Mountain Pass and Linking solutions for fractional Laplacian equations, July 1, 2012].
- Raffaella Servadei, “Two days on Nonlocal Operators and Applications”, Parma [Talk: Elliptic problems driven by the fractional Laplacian, October 5, 2012].
- Raffaella Servadei, Seminar days in Warsaw, Poland [Talk: On some non-local problems involving the fractional Laplace operator, November 22, 2012].
- Giampiero Palatucci, Dipartimento di Matematica e Applicazioni, Universita` degli Studi di Milano Bicocca [Talk: Asymptotics of the nonlocal perimeter functional, December 5, 2012].
- Giampiero Palatucci, “Norwegian-Italian Workshop in PDEs”, NTNU Trondheim [Talk: Sobolev embeddings and concentration-compactness alternative for fractional Sobolev spaces, December 12, 2012].
- Giampiero Palatucci, Dipartimento di Matematica, Universita` Sapienza di Roma [Talk: Asymptotics of the nonlocal perimeter functional, January 14, 2013].
- Raffaella Servadei, Universita Mediterranea, Reggio Calabria [Talk: Nonlocal fractional Laplacian equations, Meeting on Mathematics, January 24, 2013].
- Giampiero Palatucci, Departamento de Matematicas, Universidad Carlos III de Madrid (UC3M) [Talk: Asymptotics of the nonlocal perimeter functional, February 14, 2013].
- Giampiero Palatucci, Departamento de Matematicas, Universidad Autonoma de Madrid [Talk: Lack of compactness in (critical) fractional Sobolev embeddings, February 18, 2013].
- Giampiero Palatucci, “Winter School on Fast and Anomalous Diffusion”, Univ. Sapienza Roma [Talk: Asymptotics of the nonlocal perimeter functional, February 20, 2013].
- Agnese Di Castro, “Winter School on Fast and Anomalous Diffusion”, Univ. Sapienza Roma [Talk: Fractional regularity for nonlinear problems with measure data, February 22, 2013].
- Giampiero Palatucci, Dipartimento di Matematica e Informatica, Universita` degli Studi di Parma [Talk: Asymptotics of the nonlocal perimeter functional, March 14, 2013].
- Agnese Di Castro, Dipartimento di Matematica Applicata “U. Dini”, Univ. Pisa [Talk: Regularity results for some nonlinear elliptic problems with measure data, April 17, 2013].
- Agnese Di Castro, Departamento de Matematicas, Universidad Carlos III de Madrid (UC3M) [Talk: Regularity results for some nonlinear elliptic problems with measure data, April 23, 2013].
- Giampiero Palatucci, Dipartimento di Matematica e Informatica, Seconda Universita` di Napoli [Talk: Improved Sobolev embeddings and concentration-compactness for fractional Sobolev spaces, April 24, 2013].
Pubblications:
- A. Di Castro, G. Palatucci: Fractional regularity for nonlinear elliptic problems with measure data - to appear in J. Convex Anal. 20 (2013), no. 3.
- S. Dipierro, G. Palatucci, E. Valdinoci: Existence and symmetry results for a Schrödinger type problem involving the fractional Laplacian - to appear in Le Matematiche (Catania) 68 (2013), no. 1.
- S. Dipierro, A. Figalli, G. Palatucci, E. Valdinoci: Asymptotics of the $s$-perimeter as $s \searrow 0$ - Discrete Contin. Dyn. Syst. 33 (2013), N. 7, 2777--2790.
- A. Fiscella, R. Servadei, E. Valdinoci: A resonant problem for non-local elliptic operators - preprint
- A. Fiscella, R. Servadei, E. Valdinoci: Asymptotically linear problems driven by fractional Laplacian operators - preprint
- G. Molica Bisci, R. Servadei: A bifurcation result for non-local fractional equations - preprint
- G. Molica Bisci, R. Servadei: Lower semicontinuity of functionals of fractional type and applications to nonlocal equations with critical Sobolev exponent - preprint
- G. Palatucci, A. Pisante: Improved Sobolev embeddings, profile decomposition, and concentration-compactness for fractional Sobolev spaces - preprint
- G. Palatucci, Y. Sire: Subcritical approximation of Yamabe type non local equation: a Gamma-convergence approach - preprint
- R. Servadei: The Yamabe problem in a non-local setting - preprint
- R. Servadei, E. Valdinoci: Variational methods for non-local operators of elliptic type - to appear in Discrete Contin. Dyn. Syst. 33 (2013), no. 5.
- R. Servadei, E. Valdinoci: Fractional Laplacian equations with critical Sobolev exponent - preprint
- R. Servadei, E. Valdinoci: Weak and viscosity solutions of the fractional Laplace equation - to appear in Publ. Mat.
- R. Servadei: Infinitely many solutions for fractional Laplace equations with subcritical nonlinearity - preprint
- R. Servadei, E. Valdinoci: On the spectrum of two different fractional operators - preprint