Open Problems in Pluripotential Theory — Question 17

Definitions and mathematical statement

The supplied record attributes the following request to Blocki--Kołodziej: find a proof, relying on partial differential equation (PDE) techniques, of the estimate referred to in Question 17 as "the above estimate."

The referenced estimate and its preceding context are absent from the supplied record. Consequently, its mathematical objects, hypotheses, domains, quantifiers, constants, and boundary conditions cannot be specified, and no self-contained mathematical statement can be recovered from this evidence. The record also says that no PDE proof of "the above fact" is known; this is a supplied source assertion, not an independently verified assessment. The precise intended meaning of a proof relying on PDE techniques is not specified.

Short English statement

The request is to prove an earlier estimate using PDE techniques. Because that estimate is missing, the supplied record does not determine a precise mathematical target.

Sources

• Local UnsolvedMath registry, permanent ID $800886$, source code catalogue entry, title: Open Problems in Pluripotential Theory --- Question 17. The supplied registry labels the problem open; this status has not been independently verified.
• Dinew, Guedj, Zeriahi, Open Problems in Pluripotential Theory (2015), Question 17. Supplied source URL: https://arxiv.org/abs/1511.00705. The background records extraction by arxiv_latex and an access date of 2026-10-16; these are supplied provenance details, not a claim of independent source access.
• The supplied question carries the attribution Blocki--Kołodziej. The registry lists Dinew, Guedj, Zeriahi as proposers and 2015 as the proposed year. The preceding estimate is not included in the supplied extraction.