This article is cited in 4 papers

Embedding theorems and a variational problem for functions on a metric measure space

N. N. Romanovskiĭ

Sobolev Institute of Mathematics, Novosibirsk, Russia

Abstract: We use a new method to prove the Sobolev embedding theorem for functions on a metric space and study other questions of the theory of Sobolev spaces on a metric space. We prove the existence and uniqueness of solution to a variational problem.

Keywords: Sobolev classes, Nikol'skiĭ classes, functions on a metric space, embedding theorems, compactness of the embedding, variational problem.

UDC: 517.518+517.518.23

Received: 06.08.2013

 English version: Siberian Mathematical Journal, 2014, 55:3, 511–529

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