4 problems

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Logunov–Malinnikova's propagation-of-smallness conjecture for gradients
Logunov–Malinnikova's conjecture. Since the critical set where $| abla f|=0$ has codimension $2$ , the correct condition on $E$ should be that it has positive $(n-2+delta)$ -dimensio…
Conjectureopenelliptic-equations harmonic-functions propagation-of-smallnessarXiv posted 2 days ago
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Propagation of smallness for gradients from $(d-2+\delta)$ -Hausdorff content
Propagation-of-smallness conjecture. The propagation of smallness for $|\nabla u|$ should hold from sets of positive $(d-2+\delta)$ -Hausdorff content for every $\delta>0$ .
Conjectureopenelliptic-equations hausdorff-content propagation-of-smallnessarXiv posted 2 days ago
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Optimality conjecture for the explicit harmonic family $S_k$
$S_k$ optimality conjecture. Let $C>0$ . Then
Conjectureopendiscrete-analysis harmonic-functions propagation-of-smallnessarXiv posted 2 days ago
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Sharp error-term conjecture for discrete harmonic propagation of smallness
Sharp error-term conjecture. For all $\varepsilon>0$ , $n0 a0in N$ , $C0$ and $d a0geq 2$ , there exists a harmonic function $u: mathbb{Z}^d to mathbb{R}$ such that
Conjectureopenharmonic-functions lattice-analysis propagation-of-smallnessarXiv posted 2 days ago

Logunov–Malinnikova's propagation-of-smallness conjecture for gradients