Sharp Adams-type inequalities in ℝⁿ

By Bernhard Ruf, Federica Sani. 2012

80 citations recorded by the source corpus.

Adams’ inequality for bounded domains Ω ⊂ R4 states that the supremum of ∫ Ω e 32πu dx over all functions u ∈ W 2, 2 0 (Ω) with ‖Δu‖2 ≤ 1 is bounded by a constant depending on Ω only. This bound becomes infinite for unbounded domains and in particular for R4. We prove that if ‖Δu‖2 is replaced by a suitable norm, namely ‖u‖ := ‖ − Δu + u‖2, then the supremum of ∫ Ω(e 32πu − 1) dx over all functions u ∈ W 2, 2 0 (Ω) with ‖u‖ ≤ 1 is bounded by a constant independent of the domain Ω. Furthermore, we generalize this result to any W m, n m 0 (Ω) with Ω ⊆ Rn and m an even integer less than n.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/a72e9775fcddde8f649a9f337279bfea9413f450

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In Applied Mathematics

1. Jiuyi Zhu
2. Wenxiong CHEN *
3. Congming LI #

Citations in the corpus

• Improved Moser-Trudinger Inequality Involving Lp Norm in n Dimensions (2014, background): “We refer the reader to [4], [5], [7], [8], [9], [20], etc.”