Jonathan Bennett (Birmingham)

Generating monotone quantities for the heat equation

Abstract: The identification of functionals which vary monotonically as their inputs flow according to a given evolution equation is generally considered to be more of an art than a science. Such monotonicity results have many consequences and, in particular, allow for a deeper understanding of a variety of important inequalities in analysis (via the so-called "semigroup method" or "semigroup interpolation"). The purpose of this talk is to describe a simple framework within which a rich variety of monotone quantities for the heat equation on R^n may be "generated".