We prove that a sharp Moser–Trudinger inequality holds true on a conformal disc if and only if the metric is bounded from above by the Poincar´e metric. We also derive necessary and sufficient conditions for the validity of a sharp Moser–Trudinger inequality on a simply connected domain in R2.
Mancini, G., K., S. (2010). Moser-Trudinger inequality on conformal discs. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 12, N. 6, 1055-1068.
Moser-Trudinger inequality on conformal discs
MANCINI, Giovanni;
2010-01-01
Abstract
We prove that a sharp Moser–Trudinger inequality holds true on a conformal disc if and only if the metric is bounded from above by the Poincar´e metric. We also derive necessary and sufficient conditions for the validity of a sharp Moser–Trudinger inequality on a simply connected domain in R2.File in questo prodotto:
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