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.
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Original Russian Text Copyright © 2014 Romanovskiĭ N.N.
The author was supported by the Interdisciplinary Integration Project of the Siberian and Far East Divisions of the Russian Academy of Sciences (Grant No. 56) and the State Maintenance Program for the Junior Scientists and the Leading Scientific Schools of the Russian Federation (Grant NSh-921.2012.1).
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 55, No. 3, pp. 627–649, May–June, 2014.
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Romanovskiĭ, N.N. Embedding theorems and a variational problem for functions on a metric measure space. Sib Math J 55, 511–529 (2014). https://doi.org/10.1134/S0037446614030136
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DOI: https://doi.org/10.1134/S0037446614030136