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arXiv · 2302.02262

Sharp Sobolev and Adams-Trudinger-Moser embeddings on weighted Sobolev spaces and their applications

João Marcos do Ó·Guozhen Lu·Raoní Ponciano
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Abstract

We derive sharp Sobolev embeddings on a class of Sobolev spaces with potential weights without assuming any boundary conditions. Moreover, we consider the Adams-type inequalities for the borderline Sobolev embedding into the exponential class with a sharp constant. As applications, we prove that the associated elliptic equations with nonlinearities in both forms of polynomial and exponential growths admit nontrivial solutions.

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João Marcos do Ó, Guozhen Lu, Raoní Ponciano. 2023-02-04. Sharp Sobolev and Adams-Trudinger-Moser embeddings on weighted Sobolev spaces and their applications. https://doi.org/10.1515/forum-2023-0292

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