[Dottorcomp] Insalate di Matematica

Ven 28 Apr 2023 10:00:00 CEST

Dear all,

We remind you the upcoming talk of "Insalate di Matematica".
Here the details:

*Speaker:* *Simone Carano* (SISSA)

*Date and time:* *28th of April 2023, 4:00 pm (CET)*

*Information to attend*
*In presence:* The seminar will take place in room 3014, at the building
U5-Ratio, Università degli Studi di Milano Bicocca.
*Online**:* The seminar will be streamed via Webex platform at the
following link:
https://unimib.webex.com/unimib/j.php?MTID=mdea7a789816f8f1d9b775900efa6c93e
 (Insalate (46725283 from phones))

*Title**:* "Area functional and relaxation: an approach via strict
convergence in BV"

*Abstract*: Relaxation of the Cartesian area functional allows to extend in
a natural way the area of a graph to non smooth maps, and has been very
successful for scalar valued functions. Mainly for coercivity reasons, it
is reasonable to relax the area using the L1-topology. However, when the
codimension of the graph is larger than 1, an integral representation of
the L1-relaxed functional is not possible since, as suggested by De Giorgi
and proven by Acerbi and Dal Maso, the subadditivity property is very
frequently lost. In our work, we propose to relax the area with respect to
the strict convergence in BV : this simplifies the analysis, since it seems
to kill most of the nonlocality phenomena, but still requires a nontrivial
analysis. We focus on maps from the plane to the plane and give an explicit
integral representation of the BV -relaxed area for Sobolev maps valued S1 and
for a special class of piecewise Lipschitz maps, jumping on a union of
curves meeting at multiple junction points. These results were obtained in
collaboration with G. Bellettini (Siena and ICTP) and R. Scala (Siena).

*Keywords: *Area functional, relaxation, integral currents, Plateau problem.

*** We inform you that the talk will be recorded and uploaded on our
website. If you join the talk after the starting time, we kindly ask you to
ensure that your microphone and webcam are turned off ***

You can find the poster of the event in the attachment.
We are looking forward to seeing you!

For further information, please visit our website:
https://sites.google.com/view/insalate-di-matematica or contact us at
insalate.matematica a unimib.it. Find us also on our Instagram page:
https://www.instagram.com/insalate_di_matematica23/
<https://www.instagram.com/insalate_di_matematica22/>.

The organizers: Andrea Bisterzo, Simone Blumer, Alberto Cassella, Bianca
Marchionna, Andrea Rivezzi, Giovanni Siclari, Marta Tameni, Matteo
Tarocchi, Marco Zullino.

Il giorno ven 21 apr 2023 alle ore 13:00 "Insalate Di Matematica" <
insalate.matematica a unimib.it> ha scritto:

> Dear all,
>
> As part of the series of seminars "Insalate di Matematica",
> *Simone Carano* (SISSA) will give a talk.
> The speaker will deliver the talk *in presence* and the meeting will also
> be broadcasted *online* (see below for more information).
>
> Here the details:
>
> *Date and time*: *28th of April 2023, 4:00 pm (CET)*
>
> *Title*: "Area functional and relaxation: an approach via strict
> convergence in BV"
>
> *Abstract*: Relaxation of the Cartesian area functional allows to extend
> in a natural way the area of a graph to non smooth maps, and has been very
> successful for scalar valued functions. Mainly for coercivity reasons, it
> is reasonable to relax the area using the L1-topology. However, when the
> codimension of the graph is larger than 1, an integral representation of the
>  L1-relaxed functional is not possible since, as suggested by De Giorgi
> and proven by Acerbi and Dal Maso, the subadditivity property is very
> frequently lost. In our work, we propose to relax the area with respect to
> the strict convergence in BV : this simplifies the analysis, since it
> seems to kill most of the nonlocality phenomena, but still requires a
> nontrivial analysis. We focus on maps from the plane to the plane and give
> an explicit integral representation of the BV -relaxed area for Sobolev
> maps valued S1 and for a special class of piecewise Lipschitz maps,
> jumping on a union of curves meeting at multiple junction points. These
> results were obtained in collaboration with G. Bellettini (Siena and ICTP)
> and R. Scala (Siena).
>
> *Keywords*: Area functional, relaxation, integral currents, Plateau
> problem.
>
> *Information to attend in room 3014*
> The seminar will take place in room 3014, at the building U5-Ratio,
> Università degli Studi di Milano Bicocca.
>
> *Information to attend online *
>
> https://unimib.webex.com/unimib/j.php?MTID=mdea7a789816f8f1d9b775900efa6c93e
> (Insalate (46725283 from phones))
>
> *** We inform you that the talk will be recorded and uploaded on our
> website. If you join the talk after the starting time, we kindly ask you to
> ensure that your microphone and webcam are turned off ***
>
> You can find the poster of the event in the attachment.
> We are looking forward to seeing you!
>
> For further information, please visit our website:
> https://sites.google.com/view/insalate-di-matematica or contact us at
> insalate.matematica a unimib.it. Find us also on our Instagram page:* https://www.instagram.com/insalate_di_matematica23/
> <https://www.instagram.com/insalate_di_matematica23/>*
>
> The organizers: Andrea Bisterzo, Alberto Cassella, Bianca Marchionna,
> Andrea Rivezzi, Simone Blumer, Giovanni Siclari, Marta Tameni, Matteo
> Tarocchi, Marco Zullino.
>
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