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--- Summary ---
* Events: Fall Semester 2015 in Analysis, Lyon
, 19th Internet Seminar: Infinite Dimensional Analysis
* Seminars by: Dayrens, Ponsiglione, Santambrogio
* New papers by: Giacomelli, Rossi, Paoli, Heinemann, Kraus, Rizzi, Rocca, Scheven, Barilari, Schmidt, Di Castro* Modified papers by: Sprekels, Dai, Barbu, Gilardi, Ansini, Frigeri, Schimperna, De Philippis, Pratelli, Franzina, Marinoschi, Prinari, Rossi, Valdinoci, Marchese, Julin, Ruffini, Bonetti, Di Castro, Alberti, Brancolini, Feireisl, Barchiesi, Rocca, Novaga, Colli
--- Events ---
Fall Semester 2015 in Analysis, Lyon
Tuesday 1 sep 2015 -- Thursday 31 dec 2015
Lyon, France
From September 1 to December 31, 2015 a semester in Analysis will take place in Lyon, France, with the following main events:

- Workshop Analysis in Lyon (October 26-30, 2015); on Thursday October 29, Luigi Ambrosio will be awarded a "doctorat honoris causa" from the École normale supérieure de Lyon.

- Winter school on nonlinear function spaces in mathematics and physical sciences (December 14-18, 2015)

During the semester, the École normale supérieure de Lyon and the Université Claude Bernard Lyon 1 will host short and long term visitors. 

The scientific committee of the semester is the following:

- Stefano Bianchini (SISSA Trieste)

- Albert Fathi (École normale supérieure de Lyon)

- Alessio Figalli (University of Texas at Austin)

- Petru Mironescu (Université Lyon 1)

19th Internet Seminar: Infinite Dimensional Analysis
Tuesday 13 oct 2015 -- Saturday 4 jun 2016
Final Worshop in Casalmaggiore, Cremona (Italy), May 30th to June 4th 2016
The I-Sem is a well-established series of courses in the field of Mathematical Analysis.
It introduces master, Ph.D. students and postdocs to subjects related to functional analysis and evolution equations.
 
As usual, the course consists of three phases.

Phase 1 (October-February) The organisers provide a weekly lecture via the ISem website. The participants are expected to study the lecture notes, to solve the proposed problems, to post their remarks and questions in the website, and to post the solutions of the problems, in turn. Participants belonging to the same institution are encouraged to collaborate, possibly under the supervision of a senior local coordinator.

Phase 2 (February-May) The participants form small international groups to work on various projects which supplement the theory of Phase 1 and provide some applications. Each group is coordinated by a senior mathematician who provides bibliographical material and help.

Phase 3 (30 May-4 June, 2016) A final one-week workshop will be held at Istituto Santa Chiara,  Casalmaggiore, Cremona (Italy). There the teams will present their projects and some additional lectures  will be delivered by leading experts.

The virtual lecturers are Alessandra Lunardi, Michele Miranda and Diego Pallara and the topic is "Infinite dimensional analysis". For more details we refer to the page http:////dmi.unife.it//isem19.

--- Seminars next week ---
* Wednesday 28 oct 2015

time: 15:30
Aula Seminari, Dipartimento di Matematica di Pisa
Reconstruction of domains from slices using phase-field approximation.
Francois Dayrens 
Abstract. How can we reconstruct a domain when we know it only on a finite number of
slices? In the plane, given a family of segments, we search the "best" set
inclosing these segments. In the usual space, the question is the same
with a family of planar sections. First, by "the best set" we mean one
which minimises one of the following geometrical energies: its perimeter
or the Willmore energy of its boundary. We will see that the theorical
problem is not well posed but a numerical phase-field approximation seems
to give an answer... an unexpected solution. For the perimeter, this
solution does not "really" fit the slices. I will explain why we have this
solution and how we can slighty modify the phase field scheme to have what
we expect. I will give all (intuitive) definitions of concepts I use in
this talk, especially the phase-field model, and we will apply this
reconstruction to movie interpolation...

time: 17:00
Aula Seminari Dipartimento di Matematica di Pisa 
A variational approach to nonlocal and crystalline curvature flows
Marcello Ponsiglione (Dip. Mat. Univ. Roma ``La Sapienza'')
Abstract. In this seminar I will introduce a generalized notion of (local and nonlocal) perimeter and curvature. Then, I will describe the corresponding geometric flows, showing the coherence between variational methods (based on the minimizing movements approach) and viscosity methods. Finally, I will describe a new approach to existence and uniqueness of crystalline curvature flows. The results presented in this seminar are in collaboration with A. Chambolle and M. Morini.

* Thursday 29 oct 2015

time: 16:00
Sala Riunioni
Regolarità e dualità
Filippo Santambrogio (Laboratoire de Mathématiques d'Orsay, Université Paris-Sud)
Abstract. Presenterò una tecnica per dimostrare risultati di regolarità per soluzioni di problemi variazionali in dualità (e per le corrispondenti equazioni di Eulero-Lagrange) che abbiamo recentemente scoperto nascosta in un lavoro di Y. Brenier sulla meccanica dei fluidi. Dato un problema di minimizzazione $\min\{A(u), u\in X\}$ con il suo duale $\max\{-B(\phi), \phi\in Y\}$, se $u_0$ e $\phi_0$ sono le rispettive soluzioni, possiamo "testare" le relazioni primale-duale su delle traslazioni $u_h:=u_0(x+h)$ della $u_0$ ottima, ottenendo stime su $||u_h-u_0||$, e quindi regolarità Sobolev per $u_0$. Mostrerò esempi concreti, a partire dall'equazione di Poisson $\Delta u=f$, per passare poi a esempi più degeneri tipo p-Laplaciano, e poi a casi più complicati nello spazio-tempo (giochi a campo medio, Eulero incompressibile...). Questa tecnica è raramente ottimale, e dà solo risultati molto deboli (tipicamente, $H^1$), ma funziona in casi molto generali e sotto ipotesi molto deboli. 

--- New Papers ---
* Barilari, Paoli: Curvature terms in small time heat kernel expansion for a model class of hypoelliptic Hörmander operators
* Heinemann, Kraus, Rocca, Rossi: A temperature-dependent phase-field model for phase separation and damage
* Rizzi: Measure contraction properties of Carnot groups
* Di Castro, Giacomelli: The 1-harmonic flow with values into a smooth planar curve
* Scheven, Schmidt: An Anzellotti type pairing for divergence-measure fields and a notion of weakly super-1-harmonic functions
* Scheven, Schmidt: BV supersolutions to equations of 1-Laplace and minimal surface type
--- Modified Papers ---
* Rocca, Rossi: ``Entropic'' solutions to a thermodynamically consistent PDE system for phase transitions and damage
* Rocca, Rossi: A degenerating PDE system for phase transitions and damage
* Ansini, Prinari: On the lower semicontinuity of supremal functional under differential constraints
* Di Castro, Novaga, Ruffini, Valdinoci: Nonlocal quantitative isoperimetric inequalities
* Alberti, Marchese: On the differentiability of Lipschitz functions with respect to measures in the Euclidean space
* Barchiesi, Brancolini, Julin: Sharp dimension free quantitative estimates for the Gaussian isoperimetric inequality
* De Philippis, Franzina, Pratelli: Existence of isoperimetric sets with densities ''converging from below'' on $\mathbb R^N$
* Dai, Feireisl, Rocca, Schimperna: Analysis of a diffuse interface model of multispecies tumor growth
* Bonetti, Rocca: Generalized gradient flow structure of internal energy driven phase   field systems
* Barbu, Colli, Gilardi, Marinoschi, Rocca: Sliding mode control for a nonlinear phase-field system
* Frigeri, Rocca, Sprekels: Optimal distributed control of a nonlocal Cahn-Hilliard/Navier-Stokes system in 2D
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