<div dir="ltr"><font color="#000000" face="arial, sans-serif">Dear all,</font><div><font color="#000000" face="arial, sans-serif"><br></font><div dir="auto"><font color="#000000" face="arial, sans-serif">We remind you the upcoming talk of "Insalate di Matematica".</font></div><div dir="auto"><font color="#000000" face="arial, sans-serif">Here the details:</font></div><div dir="auto"><font color="#000000" face="arial, sans-serif"><br></font></div><div dir="auto"><font face="arial, sans-serif" color="#000000"><i><u>Speaker</u>:</i> <b>Simone Carano</b> (SISSA)<span> </span></font></div><span><font face="arial, sans-serif"><font color="#000000"><div dir="auto"><br></div><div dir="auto"><i><u>Date and time</u>:</i><span><span> </span></span><b>28th of April 2023, 4:00 pm (CET)</b></div></font><font color="#000000"><div dir="auto"><br></div></font></font></span><div dir="auto"><u><i><font color="#000000" face="arial, sans-serif">Information to attend</font></i></u></div><div dir="auto"><font color="#000000" face="arial, sans-serif"><i><u>In presence</u>:</i> The seminar will take place in room 3014, at the building U5-Ratio, Università degli Studi di Milano Bicocca.</font></div><div dir="auto"><font face="arial, sans-serif" color="#000000"><u><i>Online</i></u><i>:</i> The seminar will be streamed via Webex platform at the following link: <a href="https://unimib.webex.com/unimib/j.php?MTID=mdea7a789816f8f1d9b775900efa6c93e" target="_blank">https://unimib.webex.com/unimib/j.php?MTID=mdea7a789816f8f1d9b775900efa6c93e</a><span> </span>(Insalate <span dir="auto">(46725283 from phones)</span>)</font></div><font face="arial, sans-serif"><font color="#000000"><span><div><b><i><br></i></b></div><div dir="auto"><u><i>Title</i></u><i>:</i> <span style="background-color:rgb(255,255,255)"><font color="#000000">"</font>Area functional and relaxation: an approach via strict convergence in BV"</span></div></span></font><font color="#000000"><span><div dir="auto"><br></div><div dir="auto"><u><i>Abstract</i></u>: 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 L<span style="vertical-align:4pt">1</span>-topology. However, when the codimension of the graph is larger than 1, an integral representation of the L<span style="vertical-align:4pt">1</span>-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 S<span style="vertical-align:4pt">1 </span>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).</div></span></font><font color="#000000"><span><div dir="auto"><br></div><div dir="auto"><i><u>Keywords</u>: </i><span>Area functional, relaxation, integral currents, Plateau problem.</span></div></span></font><font color="#000000"><div dir="auto"><br></div><span><div dir="auto"><b>** 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 **</b><br></div><div dir="auto"><br></div><div dir="auto">You can find the poster of the event in the attachment. </div><div dir="auto">We are looking forward to seeing you! <br></div><div dir="auto"><br></div></span></font></font><div dir="auto"><font face="arial, sans-serif" color="#000000">For further information, please visit our website: <a href="https://sites.google.com/view/insalate-di-matematica" rel="noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer" target="_blank">https://sites.google.com/view/insalate-di-matematica</a> or contact us at <a href="mailto:insalate.matematica@unimib.it" rel="noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer" target="_blank">insalate.matematica@unimib.it</a>. Find us also on our Instagram page: <a href="https://www.instagram.com/insalate_di_matematica22/" rel="noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer" target="_blank">https://www.instagram.com/insalate_di_matematica23/</a>.</font></div><div dir="auto"><font color="#000000" face="arial, sans-serif"><br></font></div><div dir="auto"><font color="#000000" face="arial, sans-serif">The organizers: Andrea Bisterzo, Simone Blumer, Alberto Cassella, Bianca Marchionna, Andrea Rivezzi, Giovanni Siclari, Marta Tameni, Matteo Tarocchi, Marco Zullino.</font></div></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">Il giorno ven 21 apr 2023 alle ore 13:00 "Insalate Di Matematica" <<a href="mailto:insalate.matematica@unimib.it" target="_blank">insalate.matematica@unimib.it</a>> ha scritto:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div dir="ltr">Dear all,<div dir="auto"><br></div><div dir="auto">As part of the series of seminars "Insalate di Matematica", <b>Simone Carano</b> (SISSA) will give a talk. </div><div dir="auto">The speaker will deliver the talk <u>in presence</u> and the meeting will also be broadcasted <u>online</u> (see below for more information).</div><div dir="auto"><br></div><div dir="auto">Here the details:</div><div dir="auto"><br></div><div dir="auto"><u>Date and time</u>: <b>28th of April 2023, 4:00 pm (CET)</b></div><div dir="auto"><br></div><div dir="auto"><u>Title</u>:<span> </span><span style="background-color:rgb(255,229,153)"><font color="#000000">"</font>Area functional and relaxation: </span><span style="background-color:rgb(255,229,153)">an approach via strict convergence in BV"</span></div><div dir="auto"><br></div><div dir="auto"><u>Abstract</u>: <span style="font-family:arial,sans-serif;color:rgb(0,0,0)">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</span><span style="font-family:arial,sans-serif;color:rgb(0,0,0)"> </span><span style="font-family:arial,sans-serif;color:rgb(0,0,0)">L</span><span style="font-family:arial,sans-serif;color:rgb(0,0,0);vertical-align:4pt">1</span><span style="font-family:arial,sans-serif;color:rgb(0,0,0)">-topology. However, when the codimension of the graph is larger than 1, an integral representation of the</span><span style="font-family:arial,sans-serif;color:rgb(0,0,0)"> </span><span style="font-family:arial,sans-serif;color:rgb(0,0,0)">L</span><span style="font-family:arial,sans-serif;color:rgb(0,0,0);vertical-align:4pt">1</span><span style="font-family:arial,sans-serif;color:rgb(0,0,0)">-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</span><span style="font-family:arial,sans-serif;color:rgb(0,0,0)"> </span><span style="font-family:arial,sans-serif;color:rgb(0,0,0)">BV</span><span style="font-family:arial,sans-serif;color:rgb(0,0,0)"> </span><span style="font-family:arial,sans-serif;color:rgb(0,0,0)">: 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</span><span style="font-family:arial,sans-serif;color:rgb(0,0,0)"> </span><span style="font-family:arial,sans-serif;color:rgb(0,0,0)">BV</span><span style="font-family:arial,sans-serif;color:rgb(0,0,0)"> </span><span style="font-family:arial,sans-serif;color:rgb(0,0,0)">-relaxed area for Sobolev maps valued</span><span style="font-family:arial,sans-serif;color:rgb(0,0,0)"> </span><span style="font-family:arial,sans-serif;color:rgb(0,0,0)">S</span><span style="font-family:arial,sans-serif;color:rgb(0,0,0);vertical-align:4pt">1<span> </span></span><span style="font-family:arial,sans-serif;color:rgb(0,0,0)">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).</span></div><div dir="auto"><br></div></div><div dir="ltr"><div dir="auto"><u>Keywords</u>: <span style="color:rgb(0,0,0)"><font face="arial, sans-serif">Area functional, relaxation, integral currents, Plateau problem.</font></span></div><div dir="auto"><br></div><div dir="auto"></div><div dir="auto"><u><b>Information to attend in room 3014</b></u></div><div dir="auto">The seminar will take place in room 3014, at the building U5-Ratio, Università degli Studi di Milano Bicocca.</div><div dir="auto"><br></div><div dir="auto"></div><div dir="auto"><u><b>Information to attend online </b></u></div><div dir="auto"><a href="https://unimib.webex.com/unimib/j.php?MTID=mdea7a789816f8f1d9b775900efa6c93e" target="_blank">https://unimib.webex.com/unimib/j.php?MTID=mdea7a789816f8f1d9b775900efa6c93e</a> (<span style="color:rgb(51,51,51);font-family:arial;font-size:14px">Insalate </span><span dir="auto" style="color:rgb(51,51,51);font-family:arial;font-size:14px">(46725283 from phones)</span>)</div><div dir="auto"><br></div><div dir="auto"></div><div dir="auto"><b>** 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 **</b></div><div dir="auto"><b><br></b></div><div dir="auto"></div><div dir="auto">You can find the poster of the event in the attachment. </div><div dir="auto">We are looking forward to seeing you! </div><div dir="auto"><br></div><div dir="auto"></div><div dir="auto">For further information, please visit our website: <a href="https://sites.google.com/view/insalate-di-matematica" rel="noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer" target="_blank">https://sites.google.com/view/insalate-di-matematica</a> or contact us at <a href="mailto:insalate.matematica@unimib.it" rel="noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer" target="_blank">insalate.matematica@unimib.it</a>. Find us also on our Instagram page:<font face="arial, sans-serif"><u> <a href="https://www.instagram.com/insalate_di_matematica23/" rel="noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer noreferrer" target="_blank">https://www.instagram.com/insalate_di_matematica23/</a></u></font></div><div dir="auto"><br></div><div dir="auto"></div><div dir="auto">The organizers: Andrea Bisterzo, Alberto Cassella, Bianca Marchionna, Andrea Rivezzi, <span style="color:rgb(0,0,0)">Simone Blumer, </span>Giovanni Siclari, Marta Tameni, Matteo Tarocchi, Marco Zullino.</div></div></div>
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