GEORGE MASON UNIVERSITY
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. Martín-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


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