We exhibit sharp embedding constants for Sobolev spaces of any order into Zygmund spaces, obtained as the product of sharp embedding constants for second order Sobolev space into Lorentz spaces. As a consequence, we derive a new proof of Adams’ inequality, which holds in the larger hypotheses of homogenoeous Navier boundary contidions.

Adams' inequality and limiting Sobolev embeddings into Zygmund spaces / C. Tarsi. - In: POTENTIAL ANALYSIS. - ISSN 0926-2601. - 37:4(2012), pp. 353-385.

Adams' inequality and limiting Sobolev embeddings into Zygmund spaces

C. Tarsi
Primo
2012

Abstract

We exhibit sharp embedding constants for Sobolev spaces of any order into Zygmund spaces, obtained as the product of sharp embedding constants for second order Sobolev space into Lorentz spaces. As a consequence, we derive a new proof of Adams’ inequality, which holds in the larger hypotheses of homogenoeous Navier boundary contidions.
Adams' inequality; Best constants; Limiting Sobolev embeddings; Lorentz spaces; Trudinger-Moser inequalities; Zygmund spaces
Settore MAT/05 - Analisi Matematica
2012
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/170688
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