Equivalent Moser type inequalities in R2 and the zero mass case

2014/02/10 by Daniele Cassani, Federica Sani, Cassani, Daniele +3 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #math.FA

paper · pdf · doi:10.48550/arxiv.1402.2083

arxiv created 2014/02/10 · openalex publication_date 2014/02/10 · arxiv updated 2014/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We first investigate concentration and vanishing phenomena concerning Moser type inequalities in the whole plane which involve complete and reduced Sobolev norms. In particular we show that the critical Ruf inequality is equivalent to an improved version of the subcritical Adachi-Tanaka inequality which we prove to be attained. Then, we consider the limiting space D^1,2(ℝ²), completion of smooth compactly supported functions with respect to the Dirichlet norm ‖∇⋅‖₂, and we prove an optimal Lorentz-Zygmund type inequality with explicit extremals and from which can be derived classical inequalities in H¹(ℝ²) such as the Adachi-Tanaka inequality and a version of Ruf's inequality.

Citations

• Trudinger type inequalities in 𝐑^𝐍 and their best exponents

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