Fractional Adams–Moser–Trudinger type inequalities

By L. Martinazzi. 2015

81 citations recorded by the source corpus.

Abstract Extending several works, we prove a general Adams–Moser–Trudinger type inequality for the embedding of Bessel-potential spaces H n p , p ( Ω ) into Orlicz spaces for an arbitrary domain Ω with finite measure. In particular we prove sup u ∈ H n p , p ( Ω ) , ‖ ( − Δ ) n 2 p u ‖ L p ( Ω ) ≤ 1 ∫ Ω e α n , p | u | p p − 1 d x ≤ c n , p | Ω | , for a positive constant α n , p whose sharpness we also prove. We further extend this result to the case of Lorentz-spaces (i.e. ( − Δ ) n 2 p u ∈ L ( p , q ) ). The proofs are simple, as they use Green functions for fractional Laplace operators and suitable cut-off procedures to reduce the fractional results to the sharp estimate on the Riesz potential proven by Adams and its generalization proven by Xiao and Zhai. We also discuss an application to the problem of prescribing the Q -curvature and some open problems.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/cc9dc3e563eb456a43c860ecf1f68f567af9b630

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In Applied Mathematics

1. Pawan Kumar Mishra
2. Konijeti Sreenadh
3. Jacques Giacomoni
4. A. Ghanmi
5. Kamel Saoudi

In Mathematical Physics

1. Pawan Kumar Mishra
2. Konijeti Sreenadh
3. Jacques Giacomoni

Citations in the corpus

• Fractional elliptic equations with critical exponential nonlinearity (2016, result): “The problems of type (P) with exponential growth nonlinearities are motivated from the fractional Trudinger–Moser inequality [18], which gives the optimal constant and improves the former results of Ozawa [26], and Kozono, Sato and Wadade [15].”