Hello!(adsbygoogle = window.adsbygoogle || []).push({});

I would like to show the following: [tex]u\in C^2(U) \cap C(\bar{U})[/tex] satisfies [tex]\Delta u(x)>0[/tex] for any [tex]x\in U[/tex], then [tex] \max_U u [/tex] cannot be achieved by any point in [tex] U[/tex]. Here, [tex] u\in \mathbb{R}^n[/tex], i.e. it's not complex valued.

Apparently, one can use the Taylor expansion formula to show this. But how?

Thanks in advance!

Los

**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!

# Maximum principle for Delta u >0

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