# Tagged Questions

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### Improve Liouville's Theorem in Evans ' PDE

Here is Liouville's Theorem Suppose that $u \colon \mathbb{R}^n \to \mathbb{R}$ is harmonic and $u \geq 0$. Prove that $u$ is constant. (In this problem , instead of $u$ is bounded now $u \geq 0$ ...
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### What can you say about f if g is harmonic?

Suppose that f : R → R is such that, whenever g : $R^n$→ R is harmonic, so is f(g(x)). What can you say about f? This is my attempt , and I think f is a linear function.
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### Mean value proof in Evans PDE

Here is the proof I don't really understand about the part beginning using Green's formula. How can Du(y) become du/dv . Is is using the directional derivative formula ? Aslo how can you get/pull ...
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### Natural question about harmonic functions

Let $U$ an open, bounded and convex set in $R^n$. Let $(u_k)_{k \in N}$ a sequence of functions defined in $\overline{U}$. Suposse that each $u_k \in C(\overline{U}) \cap C^{2}(U)$ and harmonic in ...