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OP-10099Status unassessedPartial differential equations

Continuity of weakly n-harmonic maps

A question from EMS Surveys in Mathematical Sciences (2017). Problem 2.2; inspected PDF p. 4.

MSC 35B65 · Smoothness and regularity of solutions to PDEsMSC 58E20 · Harmonic maps, etc.

Editorial MSC2020 classification. Original article codes and source evidence are recorded in the literature directory.

Journal question · editorial summaryAs of 2017 source; current status unassessedSource & evidence ↓
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Problem statement

For n≥3n\geq3 and a compact closed Riemannian manifold NN, must every weakly nn-harmonic map u∈W1,n(Bn,N)u\in W^{1,n}(B^n,N) be continuous? Weak harmonicity means criticality of the nn-Dirichlet energy under variations in the target; no minimizing or stationarity assumption is added.

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Background

Editorial summary of Problem 2.2; inspected PDF p. 4 in Invitation to H-systems in higher dimensions: known results, new facts, and related open problems. Read the original for the full definitions and context.

EMS Surveys in Mathematical Sciences 4 (2017), 21–43. Original MSC2010 labels retained separately; problem mappings use valid MSC2020 codes.

Progress & source assessment

The source presents this question or research direction as unresolved at the time of writing. Current status has not been independently established. Source inspected on 2026-09-10; this date is a provenance check, not certification that the question remains open.

References
  1. [1]Armin Schikorra, Paweł Strzelecki. Invitation to H-systems in higher dimensions: known results, new facts, and related open problems. EMS Surveys in Mathematical Sciences (2017). linkProblem 2.2; inspected PDF p. 4

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