2009/09/03 by Adimurthi, K. Tintarev, Tintarev, K. · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #Analytic and geometric function theory #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory in Mathematical Physics #math.AP #math.FA
paper · pdf · doi:10.48550/arxiv.0909.0692
This version gives the credit to an independently proved result, missed in the early version, and corrects an error in one of the proofs
openalex publication_date 2009/09/03 · arxiv created 2009/09/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper raises a question about the optimal critical nonlinearity for the Sobolev space in two dimensions, connected to loss of compactness, and discusses the pertinent concentration compactness framework. We study properties of the improved version of the Trudinger-Moser inequality on the open unit disk B⊂\R2, recently proved by G. Mancini and K. Sandeep. Unlike the original Trudinger-Moser inequality, this inequality is invariant with respect to Möbius automorphisms of the unit disk, and as such is a closer analogy of the critical nonlinearity ∫ |u|2^* in the higher dimension than the original Trudinger-Moser nonlinearity.