1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Finiteness of an integral given an [itex]L^2[/itex] function

  1. Mar 9, 2013 #1
    1. The problem statement, all variables and given/known data
    Let [itex]\Omega[/itex] be a torus and [itex]g\in L^2(\Omega)[/itex] be a scalar value function. Is [itex]\int_{\Omega}{e^g}dx<\infty[/itex]?


    2. Relevant equations



    3. The attempt at a solution Not sure where to start. However, if [itex]g\in W^{1,2}(\Omega)[/itex] then I can show that the answer is yes by applying Moser-Trudinger inequality and decomposing [itex]W^{1,2}[/itex] as the direct sum of [itex]\mathbb{R}[/itex] and functions of average value zero on [itex]W^{1,2}[/itex]. Any hints are greatly appreciated.
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?