On a weighted Trudinger-Moser inequality in ℝ^N

2018/10/29 by Emerson Abreu, Abreu, Emerson, Leandro G. Fernandes +1
Mathematics · #26D10 #35B33 #46E30 #46E35 #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1810.12329

openalex publication_date 2018/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish the Trudinger-Moser inequality on weighted Sobolev spaces in the whole space, and for a class of quasilinear elliptic operators in radial form of the type Lu:=-r^-θ(r^α\vert u'(r)\vert^βu'(r))', where θ, β≥ 0 and α>0, are constants satisfying some existence conditions. It worth emphasizing that these operators generalize the p- Laplacian and k-Hessian operators in the radial case. Our results involve fractional dimensions, a new weighted Pólya-Szegö principle, and a boundness value for the optimal constant in a Gagliardo-Nirenberg type inequality.

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