Nash’s Continuity Theorem Revisited
Monday, November 2, 2015 - 11:00am - 12:00pm
Daniel Stroock (Massachusetts Institute of Technology)
Nash’s 1958 paper about the continuity of solutions to divergence form parabolic and elliptic equations contains two key ideas. The first of these is a Sobolev type inequality, and the second is an ingenious application of the Poincar ́e inequality for Gauss In this lecture, I will explain how these two ideas can be used to prove sharp versions Aronson’s estimates on the fundamental solution to the heat flows determined by non-degenerate, divergence form operators. Using techniques introduced by Moser and refined by Krylov and Safonov, one can easily derive both Nash’s continuity result and Moser’s Harnack principle.