[Dottorcomp] seminario probabilita' - 10 sett ore 14

[Enrico Priola]

*Damir Kinzebulatov*  (Université Laval)
*Recent progress on well-posedness of singular SDEs with critical drifts*

*Abstract: *In the first part of the talk, I will review the basic results
on SDEs with singular drifts. In the second part, I will discuss some
recent progress on weak and strong existence and conditional uniqueness for
SDEs with singular drifts having critical-order singularities. These drifts
either
(a) reach the critical strength of the singularities, i.e. multiplying such
a drift by a constant even slightly greater than 1 can destroy the weak
existence, or
(b) are more singular (not necessarily even in L^{2}_{\loc}(R^{1+d})) and
can have critical 1/\sqrt{t} singularities in time.
I will be referring to De Giorgi's method in L^p with p chosen sufficiently
large (in order to accommodate the strength of the singularities going up
to the critical threshold), some "fractional" Duhamel series
representations and an appropriate parabolic Adams-Krylov estimate, the
method of Röckner-Zhao of constructing strong solutions, and a "critical"
Orlicz space with gauge function \cosh - 1 that allows to treat the
Kolmogorov operator with the borderline strength of the singularities in
the drift where the L^p no longer exists.


Date and time: Thursday* September 10, 14:00-15:00 (Rome time zone)*
Place: *Aula Beltrami, Dip. Matematica, Univ. Di Pavia.*

-- 
Enrico Priola
Dipartimento di Matematica, Università di Pavia
Via Adolfo Ferrata 5, 27100 Pavia
tel +39 0382 985639