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April 24, 2017 | 2:45 p.m. - 4:00 p.m.
Category: Lecture
Location: Education, College of #179 | Map
5425 Gullen Mall
Detroit, MI 48202
Cost: Free

Speaker:  Nicolai V. Krylov, University of Minnesota

Title: Poisson stochastic process and basic Schauder and Sobolev estimates in the theory of parabolic equations

Abstract: We show among other things how  knowing Schauder  or Sobolev-space estimates for the one-dimensional heat equation allows one to derive their multidimensional analogs for equations with coefficients depending only on time variable with the {em same/} constants as in the case of the one-dimensional heat equation. The method is based on using the Poisson stochastic process. It looks like no other methods are available at this time and it is a very challenging problem to find a purely analytic approach to proving such results.  The main condition for it to work is that the equations should be commuting with space translations (more generally, should be commuting with a commutative group of affine mappings) and the estimates should be space-translation invariant as well.
Joint work with E. Priola.

For more information about this event, please contact Department of Mathematics at 3135772479 or eb1208@wayne.edu.