Young's Inequality can be restated as:(adsbygoogle = window.adsbygoogle || []).push({});

s^(x)t^(1-x)<=xs + (1-x)t where s,t>=0 and 0<x<1.

Basically i've been asked to prove this. I've been fiddling about with it for a couple of hours

to no avail.

I've tried to substitute t=e^u and s=e^v and then use partial differentiation w.r.t to v on st, but i'm not getting the required form. (I can't assume that exp is a convex function - otherwise it follows trivially)

Thanks in advance.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Young's Inequality alternative proof

**Physics Forums | Science Articles, Homework Help, Discussion**