Sobolev spaces on an arbitrary metric measure space: Compactness of embeddings

被引:8
作者
Romanovskii, N. N. [1 ]
机构
[1] Sobolev Inst Math, Novosibirsk, Russia
关键词
Sobolev class; Nikol'skii class; function on a metric space; embedding theorems; compactness of embedding;
D O I
10.1134/S0037446613020171
中图分类号
O1 [数学];
学科分类号
070101 [基础数学];
摘要
We formulate a new definition of Sobolev function spaces on a domain of a metric space in which the doubling condition need not hold. The definition is equivalent to the classical definition in the case that the domain lies in a Euclidean space with the standard Lebesgue measure. The boundedness and compactness are examined of the embeddings of these Sobolev classes into L (q) and C (alpha) . We state and prove a compactness criterion for the family of functions L (p) (U), where U is a subset of a metric space possibly not satisfying the doubling condition.
引用
收藏
页码:353 / 367
页数:15
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