Let $\Omega \subset \mathbb{R}^n$ be an open open subset. Let $u,v\colon \Omega\to \mathbb{R}$ be two functions such that at least one of them is compactly supported. Assume each of $u$ and $v$ can be presented as a difference of two bounded subharmonic functions in $\Omega$. Thus in particular the distributional Laplacians $\Delta u,\Delta v$ are well defined as signed measures on $\Omega$.

**Question.** Is it true that
$$\int_\Omega u(x)\Delta v(x) dx=\int_\Omega v(x)\Delta u(x) dx?$$

**Remark.** (1) The expressions under the both integrals are well defined as signed measures with compact support. Thus both sides make sense.

(2) The simplest unknown to me case is $n=2$.

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