Rearrangements and the Monge–Ampère equations

Rearrangements and the Monge–Ampère equations

We show that the direct counterpart of the Talenti symmetrization estimate for the Laplacian does not hold neither for the complex nor real Monge–Ampère equations. We also use this Talenti result to improve some known estimates for subharmonic functions in C , where the constant depends on the area...

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Veröffentlicht in:Mathematische Zeitschrift 2024-09, Vol.308 (1), Article 17
1. Verfasser: Błocki, Zbigniew
Format: Artikel
Sprache:eng
Schlagworte:
Harmonic functions
Mathematics
Mathematics and Statistics
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Zusammenfassung:We show that the direct counterpart of the Talenti symmetrization estimate for the Laplacian does not hold neither for the complex nor real Monge–Ampère equations. We also use this Talenti result to improve some known estimates for subharmonic functions in C , where the constant depends on the area of the domain, instead of the diameter.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-024-03557-x