[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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