3 problems

Let $\Omega\subset\mathbb{R}^n$ be an open subset, let $f$ be a real analytic function on $\Omega$, and let $T$ be a distribution on $\Omega$. Schwartz's conjecture. There exists a…

Removal conjecture. The conclusion of Theorem should hold without any auxiliary hypotheses involving associated data; that is, there should exist $C<\infty$ and $\tau>0$ such that…

Non-vanishing conjecture. If $\Delta_pu=0$ for $p>1$ and $p\ne2$, then $u\equiv 0$.