Boundary growth rates and the size of singular sets for superharmonic functions satisfying a nonlinear inequality

Boundary growth rates and the size of singular sets for superharmonic functions satisfying a nonlinear inequality

We estimate the size of the singular set on ∂ B where a positive superharmonic function satisfying a nonlinear inequality like - Δ u ≤ c u p in the unit ball B ⊂ R n blows up faster than a prescribed order.

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Veröffentlicht in:Archiv der Mathematik 2021-03, Vol.116 (3), p.335-344
1. Verfasser: Hirata, Kentaro
Format: Artikel
Sprache:eng
Schlagworte:
Harmonic functions
Mathematics
Mathematics and Statistics
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Zusammenfassung:We estimate the size of the singular set on ∂ B where a positive superharmonic function satisfying a nonlinear inequality like - Δ u ≤ c u p in the unit ball B ⊂ R n blows up faster than a prescribed order.
ISSN:0003-889X
1420-8938
DOI:10.1007/s00013-020-01551-3