加权索波列夫空间上的锐索波列夫和亚当斯-特鲁丁格-莫泽嵌入及其应用

IF 1 3区数学 Q1 MATHEMATICS

Forum Mathematicum Pub Date : 2024-01-01 DOI:10.1515/forum-2023-0292

João Marcos do Ó, Guozhen Lu, Raoní Ponciano

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引用次数: 0

摘要

我们在不假设任何边界条件的情况下，推导出一类具有潜在权重的索波列夫空间的尖锐索波列夫嵌入。此外，我们还考虑了亚当斯型不等式，用于将边界索波列夫嵌入到具有尖锐常数的指数类中。作为应用，我们证明了具有多项式和指数增长两种形式的非线性的相关椭圆方程承认非难解。

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

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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来源期刊

Forum Mathematicum 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Forum Mathematicum is a general mathematics journal, which is devoted to the publication of research articles in all fields of pure and applied mathematics, including mathematical physics. Forum Mathematicum belongs to the top 50 journals in pure and applied mathematics, as measured by citation impact.