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<h1>CVGMT Weekly Bulletin</h1>
<h2>Summary</h2>
<p><b>Events:</b> <a href='/event/336/'>Fall Semester 2015 in Analysis, Lyon</a></p>
<p><b>Seminars by:</b> <a href='/seminar/474/'>Guarino Lo Bianco</a>, <a href='/seminar/475/'>Alberti</a></p>
<p><b>New papers by:</b> <a href='/person/32/' >Garroni</a>, <a href='/person/550/' >Conti</a>, <a >Székelyhidi</a>, <a href='/person/1394/' >Cristoferi</a>, <a href='/person/1304/' >Mészáros</a>, <a >Inauen</a>, <a >Müller</a>, <a href='/person/58/' >De Lellis</a></p>
<p><b>Modified papers by:</b> <a >Spadaro</a>, <a href='/person/1810/'>Nardini</a>, <a href='/person/148/'>Iurlano</a>, <a href='/person/245/'>Focardi</a>, <a href='/person/550/'>Conti</a></p>
<p><b>Open positions:</b> <a href='/position/164/'>PhD or Post-Doc position in Dortmund, Germany</a>; <a href='/position/161/'>Post-doc at University of Cardiff (area Analysis and/or Probability)</a>; <a href='/position/166/'>3 assistant professorships in Padova (Analysis, Algebra, Numerical Analysis)</a>; <a href='/position/165/'>Postdoc position at Cardiff University </a>; <a href='/position/162/'>PhD studentships in analysis at University of Nottingham</a></p>
<h2>Events</h2>
<h3><a href='/event/336/'>Fall Semester 2015 in Analysis, Lyon</a></h3>
<p>
<i>Tuesday 1 sep 2015 -- Thursday 31 dec 2015</i><br />
<i>Lyon, France</i><br /><p>From September 1 to December 31, 2015 a semester in Analysis will take place in Lyon, France, with the following main events:
</p>
<p>- 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.
</p>
<p>- Winter school on nonlinear function spaces in mathematics and physical sciences (December 14-18, 2015)
</p>
<p>During the semester, the École normale supérieure de Lyon and the Université Claude Bernard Lyon 1 will host short and long term visitors.
</p>
<p>The scientific committee of the semester is the following:
</p>
<p>- Stefano Bianchini (SISSA Trieste)
</p>
<p>- Albert Fathi (École normale supérieure de Lyon)
</p>
<p>- Alessio Figalli (University of Texas at Austin)
</p>
<p>- Petru Mironescu (Université Lyon 1)
</p>
</p>
<h2>Seminars next week</h2>
<p><i>Wednesday 14 oct 2015</i></p>
<p>
time: 15:30<br /> sala seminari, dipartimento di Pisa<br/>
<b><a href='/seminar/474/'>The optimal reinforcement for a membrane and low congested regions.</a></b><br />
Serena Guarino Lo Bianco (Dip. Mat. Univ. Pisa)<br />
<b>Abstract.</b> <p>We study how to rigidify an elastic membrane under the action of
an exterior load $f$ and fixed at its boundary by adding a one-dimensional
reinforcement in the most efficient way; the reinforcement is described by
a one-dimensional set $S\subset\Omega$ which varies in a suitable class of
admissible choices. We consider also the dual problem of a given region
$\Omega$ where the traffic flows according to two regimes: in a region
$C$ we have a low congestion, where in the remaining part $\Omega\setminus
C$ the congestion is higher. The two congestion functions $H_1$ and $H_2$
are given, but the region $C$ has to be determined in an optimal way in
order to minimize the total transportation cost.</p>
<br /> <p>
time: 17:00<br /> Sala Seminari Dipartimento di Matematica di Pisa<br/>
<b><a href='/seminar/475/'>Sulla proprietà di Lusin generalizzata/ On a generalized Lusin property</a></b><br />
Giovanni Alberti (Dip. Mat. Univ. Pisa)<br />
<b>Abstract.</b> <p>In questo seminario descriverò alcuni risultati sulla proprietà di Lusin
generalizzata per mappe di Sobolev ottenuto in collaborazione con M.
Csörnyei, E. D’Aniello e B. Kirchheim, accennandone alcune applicazioni.
Secondo la definizione base, una mappa $f$ da $R^n$ in sé soddisfa la
proprietà (N) di Lusin se porta insiemi di misura (di Lebesgue) nulla in
insiemi di misura nulla. La formula dell’area mostra chiaramente che
questa proprietà è soddisfatta dalle mappe regolari, e anzi dalle mappe
Lipschitziane (ma non vale per le mappe $\alpha$-Hölderiane con
esponente $\alpha<1$), ed un primo risultato significativo in
quest’ambito (dovuto a Kaufman) estende la proprietà di Lusin alle mappe
nelle classi di Sobolev $W^{1,p}$ con $p>n$ (o meglio, dalle
rappresentanti continue di tali mappe).
La proprietà di Lusin può essere generalizzata come segue: una mappa $f$
da $R^n$ in $R^m$ soddisfa la proprietà di Lusin di indici
$(\alpha,\beta)$ se porta insiemi nulli rispetto alla misura di
Hausdorff $\alpha$-dimensionale in insiemi nulli rispetto alla misura di
Hausdorff di dimensione $\beta$.
Nel nostro lavoro caratterizziamo completamente gli indici
$k,p,\alpha,\beta$ tali che le mappe nelle classi di Sobolev $W^{k,p}$
soddisfano la proprietà di Lusin di indici $(\alpha,\beta)$.
Questa versione della proprietà di Lusin è essenziale nella formulazione
(e dimostrazione) della versione ottimale del teorema di Sard per mappe
di Sobolev.
</p>
<p>
Depending on the audience the seminar could be held in english.
</p>
<br />
<h2>New Papers</h2>
<p><b> Mészáros:</b> <a href='/paper/2807/'>Mean Field Games with density constraints</a></p>
<p><b> Mészáros:</b> <a href='/paper/2808/'>Density constraints in Optimal Transport, PDEs and Mean Field Games</a></p>
<p><b> Cristoferi:</b> <a href='/paper/2809/'>On local and global minimizers of some non-convex variational problems</a></p>
<p><b> De Lellis, Inauen, Székelyhidi:</b> <a href='/paper/2810/'>A Nash-Kuiper theorem for $C^{1,\frac{1}{5}-\delta}$ immersions of surfaces in $3$ dimensions</a></p>
<p><b> Conti, Garroni, Müller:</b> <a href='/paper/2811/'>Dislocation microstructures and strain- gradient plasticity with one active slip plane</a></p>
<h2>Modified Papers</h2>
<p><b> Conti, Focardi, Iurlano:</b> <a href='/paper/2443/'>Phase field approximation of cohesive fracture models</a></p>
<p><b> Focardi, Spadaro:</b> <a href='/paper/2636/'>An epiperimetric inequality for the thin obstacle problem</a></p>
<p><b> Nardini:</b> <a href='/paper/2646/'>A note on the convergence of singularly perturbed second order potential-type equations</a></p>
<h2>Open Positions</h2>
<p> <a href="/position/164/">PhD or Post-Doc position in Dortmund, Germany</a> (deadline: 15 Oct 2015) </p>
<p> <a href="/position/161/">Post-doc at University of Cardiff (area Analysis and/or Probability)</a> (deadline: 26 Oct 2015) </p>
<p> <a href="/position/166/">3 assistant professorships in Padova (Analysis, Algebra, Numerical Analysis)</a> (deadline: 29 Oct 2015) </p>
<p> <a href="/position/165/">Postdoc position at Cardiff University </a> (deadline: 2 Nov 2015) </p>
<p> <a href="/position/162/">PhD studentships in analysis at University of Nottingham</a> (deadline: 1 Dec 2015) </p>
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