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## Main Question or Discussion Point

Hello!

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]

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

Thanks in advance!

Los

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

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