Archive for 11th June 2009

Log-Sobolev Inequality

My 2009 Williams College NSF “SMALL” undergraduate research Geometry Group has the following inequality for any C^1 function on the unit interval and for any p ≥ 1:


with equality for constant functions and if p>1 only for constant functions. They conjecture that these results still hold if \pi^2 on the right-hand side is replaced by p\pi^2 (sharp).

The case p=1 is standard and follows from Wirtinger’s Inequality.

Are any inequalities like this known?