DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**Speaker:**Pablo Stinga, Department of Mathematics, Iowa State University

**Title: ***
Extension problem for fractional powers of parabolic operators and applications
*

**Abstract:**
We report recent advances in the regularity theory for fractional
nonlocal space-time equations like the master equation considered by
L. Caffarelli and L. Silvestre.
We prove a parabolic extension problem that characterizes the
fractional powers of any parabolic operator with time depending
coefficients,
including the fractional powers of the heat operator.
In particular, we recover the extension problem for the Marchaud
fractional derivative proved in a joint work with A. Bernardis,
F. J. MartÃn-Reyes and J. L. Torrea.
As a byproduct of our ideas we show novel mixed-norm estimates for
parabolic equations. The latter results not only recover previous
works by N. V. Krylov but also extend them to their fullest extent.
The results presented are based in joint works with J. L. Torrea.

**Time:** Friday, September 2, 2016, 1:30-2:20 p.m.

**Place:** Exploratory Hall, Room 4106

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491