[CvGmt News] seminari Ros-Oton e Serra 5/11
Daniele Castorina
castorin at mat.uniroma2.it
Thu Oct 31 10:43:43 CET 2013
Carissimi,
vi segnalo il prossimo doppio seminario di ED a Tor Vergata:
Martedi' 5 Novembre 2013, h 14:00, Aula Dal Passo
Xavier Ros-Oton (UPC, Barcelona)
"Boudary regularity results for integro-differential equations"
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.
Martedi' 5 Novembre 2013, h 14:45, Aula Dal Passo
Joaquim Serra (UPC, Barcelona)
"Nonlocal equations and a new proof of the old Cordes-Nirenberg
estimates."
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.
--
Daniele Castorina
Dipartimento di Matematica - Studio 1221
Università di Roma "Tor Vergata"
Via della Ricerca Scientifica 00133 Roma
email: castorin at mat.uniroma2.it
tel: +390672594653
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