Suppose $u$ and $v$ are subharmonic on a bounded domain $G$ of $\mathbb{R}^{n}$ with $n\geq2$, and $w=u-v.$ If $w$ is also subharmonic and defined everywhere on $G$ (we exclude the case $u$ or $v$ is harmonic), can we say that $u$ and $v$ differ by a constant?
2026-03-25 20:09:42.1774469382
A sum of subharmonic and superharmonic function that is subharmonic
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I don't know if I have misunderstood the question but if $v,w$ are (finite) subharmonic and $u=v+w$ then the hypothesis is satisfied, right?