局部紧交换群上的Sobolev空间
Sobolev spaces on locally compact abelian groups
摘要：
受一类弦论感兴趣的非线性方程的启发，我们在任意局部紧交换群上引入Sobolev空间，并研究了它们的一些性质。具体来说，我们专注于类似物的Sobolev嵌入和Rellich-Kondrachov紧性定理。作为应用，我们证明了任意紧交换群上的广义欧几里德玻色弦方程连续解的存在性。
英文摘要：
Motivated by a class of nonlinear equations of interest for string theory, we introduce Sobolev spaces on arbitrary locally compact abelian groups and we examine some of their properties. Specifically, we focus on analogs of the Sobolev embedding and Rellich- Kondrachov compactness theorems. As an application, we prove the existence of continuous solutions to a generalized euclidean bosonic string equation possed on an arbitrary compact abelian group.
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