0
$\begingroup$

If $u$ is only continuous and satisfies Mean value property , is it true that $u$ is harmonic in $\Omega \subset \mathbb{R}^n$ . $\Omega$ is bounded and open. What basically here should I know to prove it . Hints are appreciated . Thanks

  • 0
    What is $\Omega$? What exactly do you intend by mean value property?2012-07-11
  • 0
    @DavideGiraudo : i've edited.2012-07-11
  • 0
    Roughly speaking, you need to approximate $u$ by mollifiers, and then use the Mean Value Property to show that $u$ is harmonic. I learned this many years ago, and I have no reference right now.2012-07-11

3 Answers 3