Trudinger-Moser embeddings on weighted Sobolev spaces on unbounded domains

2023/05/31 by João Marcos Ó, Guozhen Lu, O, Joao Marcos do +3 · 2 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2306.00194

openalex publication_date 2023/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish embeddings on a class of Sobolev spaces with potential weights on unbounded domains. Our results provide embeddings into weighted Lebesgue spaces L^q_θ with radial power weights and establish the existence and non-existence of the maximizers for their Trudinger-Moser type inequalities. We also sharpen the maximal integrability by ``removing" necessary terms from the exponential series while maintaining the continuity of the embedding.

Cited by

• Fractional Trudinger-Moser type inequalities with logarithmic convolution potentials
• Minimizers and best constants for a weighted critical Sobolev inequality involving the polyharmonic operator

Related

• Sharp Sobolev and Adams–Trudinger–Moser embeddings on weighted Sobolev spaces and their applications
• Weighted Trudinger-Moser inequalities in the subcritical Sobolev spaces and their applications
• On a weighted Trudinger-Moser type inequality on the whole space and related maximizing problem
• On a weighted Trudinger-Moser inequality in ℝ^N
• An idea on proving weighted Sobolev embeddings