Mathematics

Generalized Sobolev spaces and embedding theorems

N. N. Romanovskii

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: A scale of Sobolev-type spaces is constructed including classical Sobolev and Sobolev-Slobodetskii spaces, spaces consisting of Sobolev functions satisfying certain differential relations. This approach allows one to define Sobolev spaces for functions defined on a topological space and to prove embedding theorems.

Key words: Sobolev spaces, embedding theorems, topological spaces, differential relations.

UDC: 517.518+517.518.23

Received: 11.10.2024

DOI: 10.55959/MSU0579-9368-1-66-6-5