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arXiv · 2306.00194

Trudinger-Moser embeddings on weighted Sobolev spaces on unbounded domains

Joao Marcos do O·Guozhen Lu·Raoni Ponciano
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Abstract

We establish embeddings on a class of Sobolev spaces with potential weights on unbounded domains. Our results provide embeddings into weighted Lebesgue spaces $L^q_\theta$ 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.

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Joao Marcos do O, Guozhen Lu, Raoni Ponciano. 2023-05-31. Trudinger-Moser embeddings on weighted Sobolev spaces on unbounded domains. https://doi.org/10.3934/dcds.2024103

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