<html>
<head>
<meta http-equiv="content-type" content="text/html; charset=ISO-8859-15">
</head>
<body text="#000000" bgcolor="#FFFFFF">
Carissimi,<br>
<br>
vi segnalo il prossimo doppio seminario di ED a Tor Vergata:<br>
<br>
<h2><small>Martedi' 5 Novembre 2013, h 14:00, Aula Dal Passo </small></h2>
<small>
</small>
<h2><small>Xavier Ros-Oton (UPC, Barcelona)
</small></h2>
<small>
</small>
<h2><small>"Boudary regularity results for integro-differential
equations"<br>
<br>
We study the boundary behavior of solutions to elliptic
integro-differential equations. First we prove that, for the
fractional Laplacian $(-\Delta)^s$ with $s\in (0,1)$, solutions
$u$ are comparable to $d^s$, where $d(x)=dist(x,\partial\Omega)$
is the distance to the boundary of the domain. Moreover, we show
that $u/d^s$ is H\"older continuous up to the boundary, and that
$u/d^s|_{\partial\Omega}$ plays the role that the normal
derivative plays in second order elliptic equations. Finally, we
also present new boundary regularity results for fully nonlinear
integro-differential equations.</small></h2>
<small><br>
</small>
<h2><small>Martedi' 5 Novembre 2013, h 14:45, Aula Dal Passo </small></h2>
<small>
</small>
<h2><small>Joaquim Serra (UPC, Barcelona) </small></h2>
<small>
</small>
<h2><small>"Nonlocal equations and a new proof of the old
Cordes-Nirenberg estimates."<br>
<br>
We will briefly discuss the motivation of fully nonlinear
integro-differential equations from the perspective of
stochastic differential control and games, putting the emphasis
in financial modeling.
Next, we will explain the equivalent to an elliptic equation
with bounded measurable coefficients in the nonlocal context,
and why the proof of Holder regularity of solutions is much more
elementary when the order of the equation is less that 2.
Finally, we will give a new short proof of the old second order
Cordes-Nirenberg estimates in which the regularity for the local
equation is obtained by factorizing it into two nonlocal
equations. As in the original result, we obtain an explicit
pinch condition for the eigenvalues of the coefficient matrix.
Similar ideas gives also new Cordes-Nirenberg type results for
integro-differential equations.</small></h2>
<br>
<pre class="moz-signature" cols="72">--
Daniele Castorina
Dipartimento di Matematica - Studio 1221
Università di Roma "Tor Vergata"
Via della Ricerca Scientifica 00133 Roma
email: <a class="moz-txt-link-abbreviated" href="mailto:castorin@mat.uniroma2.it">castorin@mat.uniroma2.it</a>
tel: +390672594653</pre>
</body>
</html>